Place the destemmed and deseeded ancho and guajillo chiles, tomatoes, onion, garlic, oregano, chili flakes, and a generous pinch of salt in a medium pot, then pour in the chicken broth.
Place the pot over medium-high heat and bring to a gentle boil, then reduce the heat to medium and simmer for 15 minutes, or until the tomatoes and peppers are soft.
Remove the skins from the tomatoes and discard.
Transfer the softened peppers, tomatoes, onion, and garlic to the bowl of a blender and add 1 cup of the cooking liquid; set the remaining cooking liquid aside.
Blend on high for 1-2 minutes or until the sauce is smooth and homogenous; if the sauce is too thick, add more of the cooking liquid, 1-2 tablespoons at a time, as needed.
Heat 1 tablespoon of oil in a skillet set over medium heat.
Once the oil is hot, carefully pour in the sauce (it may sputter a bit), and stir a few times to distribute the oil, then reduce the heat to medium-low and let simmer for 6-8 minutes or until the sauce starts to thicken; stir frequently to prevent sticking.
While the sauce is reducing, scramble the eggs to your preferred doneness.
Taste the sauce and adjust for salt and pepper if needed, then add the tortilla chips to the sauce and gently fold them in until all of the chips are coated; cut the heat.
Layer the chilaquiles with the scrambled eggs, then garnish with whichever toppings you’re using.
Serve immediately and enjoy!