Preheat oven to 350 degrees. Place the tortilla chips on a sheet pan and cook for 5 minutes.
Heat the oil in a large skillet. Add the enchilada sauce and cook, stirring, for 2 minutes. Reduce the heat to medium-low. Whisk the eggs with ½ teaspoon salt and ½ teaspoon pepper. Pour into the hot sauce and cook, stirring occasionally, until the eggs are fully incorporated into the sauce and set, about 10 minutes. Add the tortillas back into the pan and stir to make sure they are fully coated with sauce.
Top with the cilantro and cheese and serve immediately. Serve with salsa on the side.