When you need a real brunch—one that cures your morning-after spell, fills you up for the day, or just generally makes you feel in top form—you should eat chilaquiles. They are fried and sauced tortilla triangles topped with everything in the Mexican-topping catalogue, from queso fresco and avocado, to sliced white onions and pink radish disks. The combination of rich flavors and contrasting textures has made chilaquiles beloved throughout Mexico and beyond. Everyone knows it’s the ultimate brunch dish.

Chilaquiles just means “broken-up old sombrero,” according to Mexican cookbook author Diana Kennedy. You definitely need tortillas—they’re the sombreros. But beyond that, there’s plenty of room for creativity: Not only does every region have its own special way of preparing chilaquiles, but the variations break down to the household level.

Here’s how to make the best platter of chilaquiles for your next brunch.

1. The Tortillas

1_tortillasChilaquiles depend on stale corn tortillas for their very existence. In traditional Mexican cooking, you buy or make fresh tortillas daily. Those fresh tortillas are step one in making the best tacos. But the next day, when there’s still a pile of flatbreads in the kitchen, you’ve got to find a way to use them up. Wasting zero tortillas is the incentive for other Mexican dishes in addition to chilaquiles, like tortilla chips and gordas (cakes made from ground-up tortillas).

Though you’re using them stale, the key is to start with the best tortillas—ones that don’t have preservatives and therefore can get stale in the first place. If you’re getting industrial tortillas from the supermarket, you’re probably not experiencing either peak freshness or peak staleness. To get fresh tortillas to go stale, put them on the counter and wait 12 hours. To make enough chilaquiles to feed six brunchers, start with 16 tortillas that are about 6 inches in diameter. Cut them into six wedges each.

2. Frying

2_fryingChilaquiles aren’t crispy in the end, but frying your tortilla wedges is still a key step. Heat a few inches of oil in a pan over medium-high heat. When you think the oil is hot, throw in one triangle; when it sizzles a lot, add enough to fill up your pan without crowding it. Cook the tortilla wedges until they’re golden, about a minute each. If you have enough oil in there, you won’t need to flip them. Transfer finished chips to paper towels to drain, and dust them with salt while they’re still hot. Keep frying in batches until all the triangles are golden. You can do this an hour or two in advance.

If you’re making chilaquiles for a crowd and frying strikes you as daunting, you can also toast the tortilla triangles in the oven. Preheat to 425 degrees Fahrenheit and toss the tortillas with olive oil and salt. Arrange them more or less in one layer and bake for 20 minutes, until golden. In a pinch, you can use a bag of store-bought tortilla chips, but know they won’t hold up to the sauce nearly as well. The result will be more like pudding.

3. Chilaquiles Verdes

3_green sauceLike enchiladas or huevos divorciados, chilaquiles come in green and red variations. The green is at once milder and tangier, and it’s made from tomatillos that can be roasted, boiled quickly, or used raw. Remove the husk and wash off the stickiness, then blend the tomatillos (prepared as you like) with cilantro, garlic, white onion, and jalapeños. Season with lime juice and salt to taste. With two pounds of tomatillos, four cloves of garlic, half of a white onion, and a couple of jalapeños, you’ll have plenty to coat your 16 tortillas’ worth of chips. Transfer the sauce to a large pot and bring it to a simmer with a cup of water or chicken broth to get it ready for your crispy tortillas.

4. Chilaquiles Rojos

4_red sauceA red sauce has a tomato base, but that’s not its real source of flavor. A few dried chiles—like mild pasillas or guajillos, or hotter chiles de árbol—will ensure your sauce smacks of Mexico, not Italy. You can toast the chiles for extra flavor, then remove the stems and soak them in hot water until pliant, about 30 minutes. Blend the chiles with the same staples as for green sauce—garlic, cilantro, jalapeño, cilantro, and salt—then add a 28-ounce can of whole tomatoes. Pour this into a stockpot and add a cup of water or broth to finish up your rojo version.

5. Soft or Crunchy

5_soft or chewyThe next step is to add your tortillas to your sauce. The longer the chips sit in the sauce, the soggier they will be. “There are two kinds of people in Mexico,” writes Pati Jinich, author of Pati’s Mexican Table. “Those who like their chilaquiles crispy and those who like them soft.” She’s in the first group. To preserve the crisp edges of your chips, toss the chips with the sauce just before serving. If you’re in the second club (as I am), you can let your chips sit in the sauce for 10 minutes or more, until they collapse and soak up lots of sauce and flavor. In this case, your chilaquiles will resemble a sopa seca, or “dry soup.”

6. Meat

6_chickenIf you want to bulk up your chilaquiles with meat, be frugal about it. The cuisine of leftover tortillas is a peasant cuisine at heart, and if you’re being resourceful, you’re probably not going out and buying expensive steaks. You can simmer a little bit of leftover cooked pork, brisket, or chorizo in your sauce before you add the chips. If you haven’t thought that far ahead, add two to three boneless, skinless chicken breasts to the simmering sauce and cook until done, about 15 minutes. Remove the chicken, shred the meat, and return to the sauce before throwing in the chips.

7. Eggs

7_eggAs brunch food, chilaquiles love to get an egg on top. If you’re cooking for one or two, fry eggs to your liking on the side, then relocate them to crown the chilaquiles. If you’ve got a bigger crowd, arrange the sauced chilaquiles on a baking sheet and carefully crack eggs on top. Bake in a 400°F oven for about 10 minutes, until the whites are done to your liking.

8. Creamy Toppings

8_creamy toppingsUp until now, your chilaquiles have been a two-ingredient dish, more or less: fried tortillas and spicy, tangy sauce—with the option of meat or egg. Yes, there are variations in the method, but it’s in choosing the toppings that you can make this dish your own. Also, chilaquiles can look quite humble, so if you want to spruce things up for guests, toppings double as essential decorations. You don’t have to use everything here; start with one or two garnishes, depending on what’s on hand already and what you like.

Creamy toppings balance out the spice in the sauce. Avocado—cubed or made into guacamole—queso fresco, and sour cream (or crema or even plain yogurt) all add the right richness.

9. Crunchy Toppings

9_crunchy toppingsEspecially if you’ve opted for soft-ish chilaquiles, choose some of your garnishes for their textural contrast. Thinly sliced radishes are traditional, as are slices or cubes of white onion. In season, you could try sprinkling fresh corn kernels cut off the cob.

10. Bright Toppings

10_bright toppingsFinish off the ultimate brunch dish with bright, light trimmings: sprigs of cilantro, wedges of lime for eaters to squeeze themselves, and sliced jalapeños. You can throw on the jalapeños fresh, or quick-pickle them in a mix of vinegar, salt, and sugar, brought to a boil and poured over the slices 30 minutes in advance.

Be sure to impress, next time you get together for brunch with friends, by whipping up this killer chilaquiles recipe.