Add olive oil, turkey, bell peppers, and onion to a large skillet. Cook over medium heat for 10-15 minutes, stirring occasionally and breaking up the meat with a spatula, until the turkey is fully cooked and the vegetables are tender.
Drain excess grease from your meat if needed, then stir in onion powder, garlic powder, salt, and black pepper. Cook for 1–2 minutes, stirring continuously, until the seasonings are well incorporated.
Reduce heat to low. Add ketchup, BBQ sauce, brown sugar, mustard, and Worcestershire sauce. Stir until fully combined.
Increase heat back to medium and bring the mixture to a simmer. Cook for 5–10 minutes, stirring frequently, until the sauce thickens to your desired consistency.
Serve warm on hamburger buns. Makes approximately 6 sandwiches.