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 the olive oil over the chicken breasts and then coat them evenly with the spice mixture.
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 cooking, 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 and serve with lime wedges on the side.