Melt butter over medium-high heat in a large pan. Add onion and bell pepper and cook until they are starting to soften but still have a little crunch.
Add chipotle peppers, red pepper flakes, paprika and season to taste with salt and pepper.
Stir leftover short ribs into onion mixture and transfer to a bowl.
Wipe pan clean. For each quesadilla, sprinkle about 1/4 cup cheese on a tortilla, top with 1/4 of short rib/onion mixture, and cover with another 1/4 cup cheese. Place a second tortilla on top.
Melt about a 1/2 tablespoon butter in the pan, add quesadilla and cook until golden brown on each side and cheese is melted. Repeat for remaining 3 quesadillas.