01 - Combine salsa verde, olive oil, cumin, garlic powder, smoked paprika, salt, and black pepper in a medium bowl until well blended.
02 - Place chicken breasts in a large ziplock bag or shallow dish. Pour half the salsa verde mixture over the chicken, reserving remaining portion for grilling. Refrigerate for 30 minutes to 4 hours.
03 - Heat grill to medium-high (375-400°F). Lightly oil grates to prevent sticking.
04 - Remove chicken from marinade and discard used liquid. Grill covered for 5-7 minutes per side until internal temperature reaches 165°F and juices run clear.
05 - During final 2 minutes of grilling, spoon reserved salsa verde over each breast and distribute Pepper Jack cheese evenly. Close lid to melt cheese.
06 - Transfer to serving platter. Garnish with fresh cilantro and lime wedges.