In a large bowl, combine salsa verde, olive oil, lime juice, cumin, salt, and black pepper.
Add the chicken breasts to the bowl and toss to coat evenly with the marinade. Cover and refrigerate for at least 30 minutes, or up to 2 hours.
Preheat the grill to medium-high heat.
Remove the chicken from the marinade and discard any remaining marinade.
Grill the chicken for 4-5 minutes per side, or until fully cooked through (internal temperature of 165°F).
During the last minute of grilling, place a slice of pepper Jack cheese on each chicken breast and close the grill lid to melt the cheese.
Remove the chicken from the grill and let rest for a few minutes.
Garnish with fresh cilantro and serve with lime wedges, if desired.