Preheat the oven to 425 degrees F.

Cook and stir beef in a skillet over medium heat until browned, 5 to 7 minutes. Add onions and bell peppers; cook and stir until softened, 5 to 10 minutes. Pour barbeque sauce over beef mixture and simmer until sauce is slightly reduced, about 10 minutes.

Lay 4 tortillas on a baking sheet; top each with beef mixture, Cheddar cheese, and remaining tortillas.

Bake in the preheated oven for 10 minutes. Flip quesadillas and cook until cheese is melted, about 5 minutes more.