01 - In a medium bowl, whisk together the salsa verde, olive oil, ground cumin, garlic powder, smoked paprika, salt, and black pepper until well combined. Divide the mixture in half, reserving one portion for later use during grilling.
02 - Place the chicken breasts in a large resealable plastic bag or shallow dish. Pour half of the salsa verde mixture over the chicken, ensuring each piece is evenly coated. Seal and refrigerate for at least 30 minutes, or up to 4 hours for deeper flavor penetration.
03 - Preheat an outdoor grill or grill pan to medium-high heat. Lightly oil the grates to prevent the chicken from sticking during cooking.
04 - Remove the chicken from the marinade and discard any used marinade. Place the chicken on the hot grill, cover, and cook for 5 to 7 minutes per side until the internal temperature reaches 165°F and the juices run clear.
05 - During the final 2 minutes of grilling, spoon the reserved salsa verde mixture over each chicken breast. Top evenly with the shredded Pepper Jack cheese. Close the grill lid and allow the cheese to melt completely.
06 - Transfer the chicken to a serving platter. Garnish with chopped fresh cilantro and serve immediately alongside lime wedges for squeezing.