Preheat your grill to medium-high heat. If using a grill pan, heat it over medium heat on the stovetop.
In a small bowl, mix together the olive oil, garlic powder, onion powder, cumin, smoked paprika, salt, and 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 cooking, spoon salsa verde over each chicken breast and top with shredded pepper jack cheese. Close the grill lid to melt the cheese for about 2-3 minutes.
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.