Breakfast Chilaquiles with Fried Eggs

Steps

1. Preheat the oven to 400°F (200°C). Cut each tortilla into 6 wedges, toss them in a large bowl with the oil and 1/2 teaspoon of the salt, and spread them in a single layer on two sheet pans. Bake for 12 to 15 minutes, swapping the pans halfway, until golden and brittle. They crisp further as they cool; set a small handful aside for the end.
2. Meanwhile, pull the husks off the tomatillos and rinse them under warm water to remove the sticky film. Cut half the onion into large chunks and finely chop the other half. Stem the jalapeños and seed them if you want a mild sauce.
3. Put the tomatillos, onion chunks, jalapeños, and peeled garlic in a saucepan, cover with the water, and bring to a simmer. Cook for 8 to 10 minutes, until the tomatillos turn olive green and give under a spoon without bursting. Drain and blend with half the cilantro, stems included, and 1/2 teaspoon of the salt until smooth.
4. Remove the chorizo from its casing. Heat a 12-inch (30 cm) cast-iron skillet over medium-high heat and cook the chorizo for 6 to 8 minutes, breaking it up with a spatula, until you have browned, crisp crumbles sitting in their red fat. Lift them out with a slotted spoon onto a plate and leave about 1 tablespoon of fat in the skillet.
5. Pour the salsa verde into the hot fat, standing back because it spatters. Fry it for 4 minutes, stirring: it darkens and thickens. Add the broth and simmer for 5 minutes, until it has the consistency of heavy cream: it should stay fairly loose, since the chips will soak it up. Taste, adjust the salt, and pour 4 tablespoons of the salsa into a small bowl for the table.
6. Prep the toppings while the sauce simmers: chop the rest of the cilantro, crumble the queso fresco, cut one lime into wedges, and juice the other. Thin the crème fraîche with 1 tablespoon of lime juice so it drizzles from a spoon.
7. This is the moment that decides the crunch. Bring the sauce back to a gentle simmer, add all the chips at once except the reserved handful, and toss for 30 seconds, just until they are all coated. Make 4 wells, crack an egg into each, lightly salt the eggs, and cover the skillet.
8. Cook for 4 to 5 minutes over medium-low heat, until the whites are set and opaque and the yolks are still glossy and runny. The chips on the bottom soften while the ones on top stay crunchy.
9. Off the heat, tuck the reserved chips around the edges, scatter the chorizo, queso fresco, chopped onion, and cilantro over the top, and drizzle with the cream. Serve right away in the skillet, with the lime wedges and the bowl of salsa verde on the side.