1) Divide turkey into 4 equal sized rounds. Make 2 equal sized patties out of each round so you have 8 patties total. Sprinkle 4 of the patties with 2 tablespoons each of roasted red peppers and cheese, and top with remaining patties working the turkey around the edges to seal burgers closed.
2) Season with salt and a few grinds of pepper. Griddle or grill until cooked through, about 5 minutes per side.