4ouncesthick homemade-style corn tortilla chipssuch as the ones you buy at a Mexican grocery
¼cupMexican queso frescocrumbled
Optional garnishes: Monterey Jack cheesesour cream, chopped onion, guacamole, chopped green onion
Toast the chile pieces a few at a time in a dry heavy skillet or on a griddle heated over medium, pressing them flat against the hot surface with a metal spatula until they are aromatic, about 19 seconds per side. Place toasted chiles in a bowl, cover with hot tap water, place a small plate on the top of the chiles to keep them submerged, and rehydrate the chiles for 20 minutes.
Use a pair of tongs to transfer the rehydrated chiles to a blender. Add the water, tomatoes, and garlic and process to a smooth puree. Press the mixture through a medium-mesh sieve into a bowl, discarding the solids (or use them in something else).
Heat a tablespoon of oil in a 4 to 5-quart pot or Dutch oven over medium-high heat. When hot, add the chile puree and stir nearly constantly until reduced to the consistency of tomato paste, about 7 minutes. Add the broth, partially cover and simmer over medium-low heat for 20 minutes. Season with sugar and salt. You should have about a generous 2 cups of brothy sauce. The sauce can be made up to this point the day before and reheated on the morning that you’re making the chilaquiles.
Raise the heat under the sauce to medium-high, return to a rolling boil. Stir in the chips, coating all of them well. Cover and turn off the heat. Let stand for 5 minutes (no longer).
While the chips are soaking, heat the remaining 1 tablespoon of the oil in a large skillet over medium heat, add the eggs, and cook on one side just until set, sunny-side up or flip to serve over-easy.
Spoon the chilaquiles onto warm plates. Garnish with the toppings of your choice. Transfer an egg to each portion and serve right away.