Preheat your grill to medium-high heat.
In a small bowl, mix together the garlic powder, onion powder, cumin, smoked paprika, salt, and black pepper. Rub this spice 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 the chicken and sprinkle the shredded pepper jack cheese on top. Close the grill lid and let the cheese melt, about 2-3 minutes.
Remove the chicken from the grill and let it rest for 5 minutes. Garnish with fresh cilantro and serve with lime wedges on the side.