Add olive oil to a medium skillet and place over medium high heat. Add in the garlic, white onion and bell pepper; sauté for 5 minutes or until onion is translucent. Transfer ingredients to a small bowl.
Next add ground turkey to the skillet and season with salt and pepper; break up the meat as it cooks.
Once turkey is cooked, add the onion/bell pepper mixture back in. Then add in ketchup, BBQ sauce, Worcestershire sauce, vinegar and mustard. If you like a little heat, add in cayenne pepper.
Stir well to combine and bring to a simmer, then reduce heat to low and cook for 10 minutes longer.
Next add cheese on top of meat mixture, cover with a lid and let the cheese melt for 2 minutes (or until melted). Transfer meat onto hamburger buns and (optional) top with any optional toppings you like.
Serve on hamburger buns and enjoy!