In a bowl, mix together the salsa verde, olive oil, garlic powder, onion powder, cumin, salt, and black pepper.

Place the chicken breasts in a resealable plastic bag or shallow dish. Pour the marinade over the chicken, ensuring it is well coated. Seal the bag or cover the dish and refrigerate for at least 30 minutes.

Preheat your grill to medium-high heat, about 400°F (200°C).

Remove the chicken from the marinade, allowing excess marinade to drip off. Place the chicken on the grill and cook for 6-8 minutes on each side, or until the internal temperature reaches 165°F (74°C).

During the last few minutes of grilling, sprinkle the shredded pepper jack cheese over the chicken and close the grill lid to melt the cheese.

Once cooked, remove the chicken from the grill and let it rest for about 5 minutes. This helps retain the juices.

Slice the chicken and garnish with fresh cilantro, if desired. Serve with lime wedges for an extra burst of flavor.