Blend together the ground turkey, onion, garlic, jalapeño, oil, 1/3 cup of barbecue sauce, paprika, chili powder, salt, and black pepper in a mixing bowl. Press the mixture into an 8x11 baking dish. Bake at 400° for 20 minutes or until temperature reaches 165°.
Slice a whole loaf of Hawaiian buns lengthwise removing the top. Layer the cheese followed by the turkey burger, the remaining barbecue sauce, and toppings. Replace the bun top and brush with melted butter. Bake for another 5-10 minutes to melt the cheese.