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.