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.
02 - Place the chicken breasts in a large resealable plastic bag or shallow dish. Pour half of the salsa verde mixture over the chicken, reserving the remainder for grilling. Seal or cover 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 sticking.
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 juices run clear.
05 - During the last 2 minutes of grilling, spoon the reserved salsa verde mixture over each chicken breast and distribute the shredded Pepper Jack cheese evenly on top. Close the grill lid to allow the cheese to melt completely.
06 - Transfer the chicken to a serving platter. Sprinkle with chopped fresh cilantro and serve immediately with lime wedges alongside.