Heat a skillet over medium-high heat. Heat tortillas 1 at a time, flipping until heated through, 1 to 2 minutes per side.
Heat vegetable oil in a separate skillet over medium heat. Crack eggs gently into skillet in a single layer, being careful not to break the yolks. Sprinkle Cheddar cheese over the eggs, avoiding putting too much cheese on the egg yolks. Cook until eggs are set and cheese is melted, 3 to 5 minutes.
Place tortillas on serving plates; spoon 1/4 cup salsa onto the center of each. Top each tortilla with tomato slices, a dollop of sour cream, and 2 cooked eggs. Season with salt and pepper.