Combine ground turkey and 1/4 cup Roasted Garlic Teriyaki, form into 8 thin patties. Separate diced cheese into 4 sections and place one cheese section on a turkey patty and the second patty on top, pinching the edges around the burger to seal the edges. Continue with remaining patties, then refrigerate 4 stuffed burgers for 20 minutes.
Pour vegetable oil in a medium saucepan, heat oil and add sliced onions. Stir onions until soft, about 3 minutes, add remaining Roasted Garlic Teriyaki and saute for an additional 2 minutes. Grill stuffed burgers and serve with sauteed onion.