Brush the tortillas on one side with the oil. Dividing evenly, form sandwiches with the tortillas (oiled-sides out) and the Cheddar.
In batches, broil the sandwiches on 2 foil-lined rimmed baking sheets until the tortillas are crisp and the cheese has melted, 1 to 2 minutes per side.
Top with the eggs. Add the salsa, scallions, and hot sauce.
Our family really enjoys this for breakfasts. We leave out the cheese, scramble the eggs and roll 'em up in the tortillas