Go traditional with chilaquiles verdes

Salsa verde
Put the tomatillos, chile, onion and garlic in a medium pot and cover with water. Bring to a boil. Simmer for about 15 to 20 minutes, until the vegetables are soft and the tomatillos turn pale green. Cool slightly.

Transfer the boiled vegetables, along with the cooking water, to a blender. Puree for a few seconds to blend; be sure to hold down the lid with a towel for safety. Add the herbs, salt and broth. Continue to puree until smooth. You should have about 1 quart of salsa verde.

Put a pot over medium-high heat and coat with the oil. When the oil is hot, pour in the tomatillo sauce, it will bubble a bit. Reduce the heat to medium and simmer for 10 to 15 minutes until the sauce is slightly thickened, stirring occasionally. Keep warm while assembling the chilaquiles.

Chips
Pour about 2 inches of oil in a heavy-bottomed pot or countertop deep fryer and heat to 375 degrees F. Stack the tortillas and fan them with your thumb to separate. Cut the tortillas into eight wedges like a pie.

Working in batches, fry the tortilla chips, turning them with a skimmer or slotted spoon so they don't stick together, until golden brown, about 2 to 3 minutes. Transfer the chips to a paper towel-lined baking pan or brown paper bag to drain. (Return the oil to the proper temperature between batches.) Cool.

Chilaquiles
Pour the salsa verde into a wide pot or pan and place over medium heat. Just when it starts to bubble, stir in the beaten eggs. Cook and stir for about 5 seconds until the egg feathers into the sauce to thicken and bind.

Immediately add the chips, tossing gently until they have absorbed enough sauce and become soft. Take care not to break the chips. Sprinkle the Jack cheese on top and let it melt.

Ranchero sauce
Combine the tomatoes, onion, chile and garlic in a blender (you may need to do this in batches). Puree for a few seconds until completely smooth. You should have about 1 quart of tomato sauce.

Heat the oil in a pot or skillet. Carefully pour in the tomato puree and fry it over high heat, it will bubble a bit. Stir in the broth and salt. Reduce to medium-low heat. Simmer until the sauce deepens in color and thickens, about 30 minutes, stirring occasionally. Remove from the heat and cover to keep warm. (Sauce can be prepared a day or two day ahead, the flavors will get better. Keep refrigerated.)

Eggs
Coat a large skillet with about a quarter inch of oil and put over medium heat. When the oil is hot, fry 1 or 2 tortillas at a time. Cook until the tortillas are lightly crisp around the edges but still pliable. Using tongs, remove and drain on a plate lined with paper towels. Also pat the tops of the tortillas to remove excess oil.

Pour out the oil from the skillet and return to medium heat. Fry the eggs, 2 at a time, until set.

Dip each tortilla in the ranchero sauce to coat and put on a plate. Place 2 eggs on top of each tortilla and spoon with more sauce. The sauce will finish cooking the yolks.

Put a 3 quart pot over medium-high heat and coat with the oil. When the oil is hot, add the onion, tomato, garlic and herbs.

Cook, stirring, until the vegetables are soft but not browned, about 5 minutes. Add the beans, broth, and enough cold water to cover by 1-inch and bring to a boil.

Reduce the heat to medium-low, cover and simmer until the beans are very tender and beginning to break down, about 2 hours. You want them to the point where they start bursting and are moist and creamy. Watch the heat carefully and stir often to prevent the beans from sticking and burning.

Season with salt and pepper before serving.

Rub the poblano peppers with a little oil and roast on a very hot grill, over a gas flame or under a broiler until the skin is blistered and blackened on all sides. Put the peppers in a bowl, cover with plastic wrap, and let sweat for about 10 minutes to loosen the skins. Peel and rub off the charred skin under cool running water, pull out the cores, and remove the seeds. Set aside.

Put the potatoes in a pot of water, add the salt and bring to a boil. Cook, uncovered, until there is no resistance when a fork is inserted into the potatoes, about 30 minutes.

Drain and return the potatoes to the pot. While the potatoes are still hot, mash them well with a potato masher. Add the butter and stir vigorously with a wooden spoon. Mix in the poblano strips and season with a generous pinch of salt.