Cook and stir ground turkey, onions, bell peppers, chile and garlic in a large skillet over medium heat until the turkey is no longer pink, about 10 minutes. Drain fat from turkey mixture.

Stir ketchup, barbeque sauce, cider vinegar, brown sugar, mustard, Worcestershire sauce and pepper into the turkey mixture. Bring the mixture to a boil, reduce heat to medium-low, and cook at a simmer until the vegetables are completely softened, about 20 minutes.

Serve on hamburger buns.