Preheat your grill to medium-high heat.
In a small bowl, mix together the olive oil, garlic powder, onion powder, cumin, salt, and pepper.
Brush the chicken breasts with the olive oil mixture on both sides.
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 top 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 if desired, then slice and serve.