Step 1Heat the oil in a large heavy-bottom saucepan over medium-low heat. Add the salt pork and cook, stirring occasionally, until it gives up most of its fat and shrivels, about 5 minutes. Add the onion and garlic and cook until they are soft and fragrant, about 3 minutes. Add the flour, and stir to evenly coat the onion and pork. Stir in the chile and the cumin and then whisk in the broth. Bring to a bare simmer and cook, stirring frequently, for 30 minutes to thicken the sauce and cook out the flour flavor. (Stir the bottom of the pan to prevent the flour from sticking and burning.) Remove from heat. Season with one-half teaspoon salt and a pinch of pepper, or to taste. This makes about 4 cups sauce. Keep the sauce warm if using immediately, or cover and refrigerate up to 2 days. Warm the sauce before using.
Step 1This works best if you set it up assembly-line fashion. Combine the cheese and onion in a large bowl. Have ready a large skillet to fry the tortillas and the saucepan of hot green chile sauce. Heat the oven to 400 degrees.
Step 2Heat 2 tablespoons oil in the large skillet over medium-high heat. Fry a tortilla on both sides until it is puffy and slightly softened, about 1 minute total. Dip the fried tortilla in the chile sauce and place it on an ovenproof plate. Sprinkle over about one-third cup of cheese and spoon over a little more chile sauce. Fry a second tortilla, dip it in sauce and place it on top of the first prepared tortilla, top it with a fried egg (if using), then spoon over more chile sauce and cheese to make 1 serving. Repeat with the remaining tortillas to make 6 servings.
Step 3Place the prepared plates in the oven and bake until the cheese melts, about 3 to 5 minutes. Serve immediately.