Quesadillas can be assembled in advance and fried quickly before serving.
Lay out 3 tortillas on a cutting board. Combine the cheddar and Monterey Jack in a small bowl. Spread a third of the cheese on each tortilla, leaving a 1-inch edge. Place the remaining 3 tortillas on top.
Melt 1/2 tablespoon butter in a 12-inch omelet pan set over medium heat, and add one filled tortilla. Cook until golden brown, 2 to 3 minutes. Flip with a spatula, and add another 1/2 tablespoon butter. Cook until browned and cheese is melted, 1 to 2 minutes more. Transfer to a cutting board. Repeat with remaining tortillas.
Cut cooked tortillas into eighths; serve immediately with salsa, if desired.