Heat the vegetable oil in a large skillet over medium heat. Fry the tortilla chips in batches until golden brown. Remove to a paper lined plate to drain any excess oil
Wipe the oil from the pan and pour the salsa verde into the skillet and bring to a gentle simmer.
Add the tortilla chips to the skillet and gently toss them with the salsa verde until they are evenly coated. Be careful not to break them up too much. Cook for 2-3 minutes, allowing the chips to soften slightly but still retain some crispness.
Remove from heat.
Divide the chilaquiles among plates and top with a fried egg.
Generously sprinkle with crumbled Gayo Azul Cotija Cheese, diced red onion, fresh cilantro.
Add any optional toppings like a dollop of sour cream, jalapeƱos or sliced avocado.