Mix the ground turkey, garlic, onion, red bell pepper, green onion, cilantro, cayenne pepper, cumin, salt, and pepper together in a bowl. Divide the mixture into 8 small patties. Place two of the pepperjack cheese quarters onto each of 4 of the patties; top with the remaining 4 patties so the cheese is in the center. Press along the edges of the burgers to seal.
Place a large skillet over medium-high heat. Cook the burgers in the skillet until no longer pink in the center and the juices run clear, about 6 minutes per side.
