Heat the oil in a large skillet over medium heat. Cook the onions, garlic, jalapenos, cumin, oregano, and some salt, until tender, about 5 minutes. Add the tomatoes and simmer until mixture thickens, about 10 minutes.
Char the tortillas slightly over the flame of a gas burner or in a dry skillet, if using an electric stove-top.
Layer some tomato sauce mixture in the bottom of a casserole dish then top with a few tortillas and 1/3 of the cheese. Repeat this ending with cheese on top. Take the remaining tortilla, roughly chop it up and scatter over the cheese. Bake until browned and sauce is bubbling around the edges.
Heat about 1/4-inch of vegetable oil in a medium skillet over medium-low heat. Fry 4 eggs in the oil, spooning the oil over the tops of the eggs to cook them without flipping.
Scoop out the enchiladas and serve with a fried egg on top.