Add the egg, shredded pepper jack, onion, garlic, cilantro, jalapeño, Worcestershire sauce, salt, smoked paprika, cumin, and black pepper to a large mixing bowl. Whisk or stir until combined.
Add the ground turkey. Gently mix with a spatula, wooden spoon, or clean hands just until the ingredients are evenly incorporated. Avoid overworking the meat.
Divide the mixture into 6 equal portions and form each into a thick, compact patty. Make a shallow indentation in the center of each burger with your thumb to encourage even cooking.
Arrange the patties on a parchment-lined plate or baking sheet. Cover and refrigerate for at least 30 minutes. This helps the Jalapeño Pepper Jack Turkey Burgers hold their shape and allows the seasonings to develop.
Lightly oil the grill grates and preheat the grill to high heat.
Place the chilled patties on the hot grill. Close the lid and cook for about 5 minutes.
Flip carefully and continue grilling for approximately 3–5 minutes, or until the center of each burger reaches 165°F (74°C).
If using additional pepper jack cheese, place one slice on each patty during the final 30–60 seconds of cooking and allow it to melt.
Rest the burgers briefly, then place them on hamburger buns and add your favorite toppings. Serve immediately.