In a large mixing bowl, combine the ground turkey, ground cumin, diced green chiles, and shredded pepper jack cheese. Season generously with salt, black pepper, and a dash of cayenne for heat. Mix until well incorporated.

Divide the mixture into four equal portions and shape each into a compact patty about ¾ inch thick. Refrigerate the patties for about 20-30 minutes to help maintain their shape.

Preheat your grill to medium-high heat, approximately 375-400°F. Lightly oil the grill grates.

Place the turkey patties onto the hot grill. Cook for about 5 minutes on one side, then flip and grill for an additional 5 minutes until the internal temperature reaches 165°F.

Remove the burgers from the grill and let them rest for a few minutes. Serve on gluten-free buns or lettuce wraps, topped with guacamole and any additional toppings.