Heat large skillet over med-high heat. Add bacon. Cook until crispy, turning once. Remove bacon to a paper towel-lined plate. Allow to cool.
Remove stem, membranes and seeds from jalapeño. Chop. Add chopped jalapeños to hot bacon grease. Cook until tender-crisp and beginning to brown, about 5 minutes. Remove with a slotted spoon and set aside. Discard any remaining grease and wipe out skillet with paper towels. Chop bacon.
Spread 1/2 Tbsp butter on one side of one tortilla. Add tortilla, butter side down, to the hot skillet. Top with 1/4 the cheese, 1/4 the bacon, and 1/4 the jalapenos. Spread butter on one side of another tortilla. Place butter side up on top of the quesadilla in skillet.
Cook 2 minutes or until browned. Carefully turn over. Cook 2 minutes on the other side or until browned. Remove from skillet and keep warm. Repeat with remaining tortillas, cheese, bacon, and jalapeños.
For gluten free, opt for gluten free, whole grain tortillas.