Begin by cutting the corn tortillas into triangle shapes. Heat the vegetable oil in a large skillet over medium heat. Once the oil is hot, fry the tortilla triangles in batches, turning them until they become crispy and golden. Transfer them to a paper towel-lined plate to drain excess oil. Season with a pinch of salt while they are still warm.
In a separate saucepan, heat the salsa verde or salsa roja over medium heat. If the sauce is too thick, you can thin it with a bit of chicken broth or water to reach your desired consistency. Simmer for 5-7 minutes to allow the flavors to meld together.
Once the salsa has simmered, reduce the heat to low. Add the fried tortilla chips to the pan and gently toss to coat them evenly in the sauce. Ensure the tortillas are well-covered but still retain some of their crisp texture. Cook for an additional 3-5 minutes, allowing the tortillas to soften slightly.
Taste the chilaquiles and adjust the seasoning if necessary, adding a pinch of salt if needed. The salsa should have a balanced, bold flavour that complements the tortillas without overpowering them.
If you're including fried eggs, now is the time to prepare them. Fry two eggs in a small pan until they reach your preferred level of doneness (sunny-side up is traditional). Season lightly with salt and pepper.
Remove the skillet from heat and prepare to serve. Spoon the chilaquiles onto individual plates, dividing the portions equally among four servings.
Top each plate of chilaquiles with crumbled queso fresco, a drizzle of sour cream or Mexican crema, and a sprinkle of diced onions and fresh cilantro. These garnishes add brightness and texture to the dish.
For an added touch of indulgence, garnish with sliced avocado and place a fried egg on top of each serving. This will elevate the dish into a complete meal. Serve immediately, as chilaquiles are best enjoyed fresh while the tortilla chips still retain some crispness.