Preheat your grill to medium-high heat.
In a bowl, combine the salsa verde, garlic powder, onion powder, cumin, smoked paprika, salt, and pepper. Mix well.
Place the chicken breasts in a large resealable plastic bag or shallow dish. Pour the salsa verde mixture over the chicken, ensuring it is well coated. Seal the bag or cover the dish and marinate in the refrigerator for at least 30 minutes, or up to 2 hours for more flavor.
Remove the chicken from the marinade and discard the marinade. Place the chicken on the preheated grill. Grill for about 6-7 minutes on each side, or until the chicken reaches an internal temperature of 165°F.
During the last few minutes of grilling, place a slice of pepper jack cheese on each chicken breast. Close the grill lid to melt the cheese.
Once cooked, remove the chicken from the grill and let it rest for 5 minutes.
Garnish with fresh cilantro and serve with lime wedges on the side.