01 - Preheat grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry with paper towels. Whisk together olive oil, cumin, smoked paprika, garlic powder, onion powder, salt, and black pepper in a small bowl. Rub seasoning mixture evenly over both sides of each chicken breast.
03 - Place chicken on the preheated grill. Cook for 5 to 7 minutes per side, turning once, until internal temperature reaches 165°F and juices run clear.
04 - During the final 2 minutes of cooking, spoon 2 to 3 tablespoons of salsa verde over each chicken breast. Place a slice of pepper jack cheese on top of each. Close grill lid and cook until cheese is melted and bubbly.
05 - Transfer chicken to a serving platter and let rest for 3 minutes. Drizzle with remaining salsa verde, sprinkle with fresh cilantro and green onions, and serve with lime wedges on the side.