Heat grill to medium-high. Oil the grill grate. In a medium bowl, combine the turkey, Gruyère, and garlic (do not overwork the meat). Form the mixture into four 3/4-inch-thick patties and make a shallow well in the top of each. Season the patties with the chili powder, 1/2 teaspoon salt, and 1/4 teaspoon pepper.

Grill the patties, turning once (do not press or flatten), until an instant-read thermometer inserted in the center registers 160° F, 6 to 8 minutes per side. Serve on rolls with the desired toppings.