Preheat your grill to medium-high heat.
In a small bowl, mix together olive oil, garlic powder, onion powder, cumin, salt, and black pepper. Rub this mixture evenly over both sides of the chicken breasts.
Place the chicken on the grill and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F.
During the last few minutes of grilling, spoon salsa verde over each chicken breast and sprinkle with shredded pepper jack cheese. Close the grill lid to melt the cheese.
Once cooked, remove the chicken from the grill and let it rest for 5 minutes.
Garnish with fresh cilantro before serving.