Spread half the peanut butter onto one side of 1 flour tortilla; top with sliced banana. Spread the remaining peanut butter on one side of the other flour tortilla; place tortilla, peanut butter-side down, on top of banana slices.
Spray cooking spray into a skillet and place skillet over medium heat. Place quesadilla into the heated skillet; cook until lightly browned, about 3 minutes per side. Cut quesadillas in half to serve.