Fry the eggs in approximately 1½ tablespoons of butter a skillet over medium heat. Season the eggs with salt and pepper
Assemble each quesadilla as follows:
1 flour tortilla, 1 slice Canadian bacon, 1 slice of American Cheese, 1 prepared egg, 4-5 asparagus spears, 1 slice of American cheese, top with another flour tortilla.
Add additional butter to the skillet and brown each quesadilla on both sides (flipping carefully) until golden brown.
Keep the prepared sandwiches in a warm oven while you prepare the remaining sandwiches.