Prepare the tortilla chips: Cut the corn tortillas into triangle wedges. You can either fry them or bake them depending on preference. For frying, heat vegetable oil in a pan over medium heat and fry the tortilla pieces in batches until they are golden and crisp. Remove them and place on paper towels to drain excess oil. If baking, spread them on a baking sheet, lightly brush with oil, and bake at 375°F (190°C) for about 10–12 minutes, flipping halfway until crisp and lightly golden.
Make the green chile sauce: In a large skillet over medium heat, pour in the green enchilada sauce and add the diced green chiles along with salsa verde if using. Stir everything together and let it gently simmer for about 5–7 minutes so the flavors can blend. Season with garlic powder, onion powder, and a pinch of salt, adjusting taste as needed. The sauce should be warm, slightly thickened, and very aromatic.
Combine chips and sauce: Add the crispy tortilla chips directly into the skillet with the warm green chile sauce. Gently toss everything together using a spatula so the chips are coated evenly. Be careful not to overmix or the chips will become too soggy too quickly—you want a mix of slightly softened edges and some still-crunchy pieces for texture.
Add the cheese: Sprinkle both mozzarella and Monterey Jack cheese generously over the coated chips. Reduce the heat to low and cover the skillet for 3–5 minutes, allowing the cheese to fully melt and become gooey and stretchy. If you want extra cheesiness, you can add a little more cheese on top just before covering.
Optional eggs: If serving with eggs, fry them separately in a pan until the whites are set but the yolks are still runny. You can also scramble them if preferred. Place the eggs on top of the chilaquiles just before serving so the yolk mixes into the sauce.
Finish and serve: Top the cheesy chilaquiles with sour cream, sliced red onions, chopped cilantro, and avocado if using. Serve immediately with lime wedges on the side for a fresh citrus kick. Enjoy while hot for the best cheesy, saucy texture.