Heat 3 inches of vegetable oil to 375°F in a in a large Dutch oven, wok or deep fryer. Adjust flame to maintain temperature. Line a large rimmed baking sheet with paper towels. Fry 1/4 of tortilla wedges, using a metal spider to agitate and turn them as they cook. Cook until bubbling slows to a trickle, chips are pale golden brown, and are very crisp, about 3 minutes. Transfer to the baking sheet and immediately season with kosher salt. Repeat with remaining batches.

Preheat broiler to high heat and set an oven rack 6 or 7 inches from flame. Heat 1 tablespoon oil in a large (12-inch) straight-sided sauté pan or cast iron skillet, set over medium-high heat. Add chorizo and cook, crumbling with a wooden spoon, until brown and cooked through. Remove to a plate and set aside. Remove excess oil, leaving 1 tablespoon. Add salsa verde and chicken broth and heat over medium heat until simmering. Add 3/4 of the chips and toss to coat. Cover and set aside while you make the eggs.

In a large non-stick pan, cook 4 eggs until whites are set but yolks are still runny, about 3 minutes. Season with salt. Transfer to a large plate.

Stir in the remaining tortilla chips to the chilaquiles pan and season to taste with salt if necessary. Sprinkle with cheese and the crumbled chorizo. Broil until cheese is melted (if using jack) and the tops of a few of the tortillas brown, 1 to 3 minutes. Divide onto plates or serve out of the pan. Top each portion with an egg, sour cream, pickled red onions. sliced radishes and cilantro, and serve immediately with lime wedges, for squeezing.