Preheat a griddle to medium-high heat, and spray with nonstick cooking spray. Place the 4 balls of beef on the griddle and press the balls down to form burger patties. Find something that is flat in your kitchen to help press down on the patties.
Cook patties to your desired doneness, about 4 minutes per side for medium. Transfer to a plate.
Spray the griddle again with cooking spray, Add a flour tortilla and top with a cheese slice and lettuce.
Place a cooked burger on top, then top with more cheese, and cup pico de gallo and a drizzle of sour cream.
Top with a tortilla and cook until golden, about 2 minutes.
Flip the quesadilla and cook for 2 minutes more. Repeat with remaining ingredients to make 4 quesadilla burgers.