Add olive oil to a medium skillet and place over medium high heat. Add in the garlic, white onion and bell pepper; saute 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. If sauce looks too thick, add in a tablespoon of water.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 top with jalapeno slices.Serve on hamburger buns with pepper jack cheese.