01 - Heat grill to medium-high temperature, approximately 400°F.
02 - Pat chicken breasts completely dry. 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 preheated grill. Cook for 5 to 7 minutes per side 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 piece. Close grill lid to allow cheese to melt completely.
05 - Transfer chicken from grill to a clean platter. Let rest for 3 minutes to allow juices to redistribute.
06 - Drizzle remaining salsa verde over the chicken. Sprinkle with fresh cilantro and sliced green onions. Serve immediately with lime wedges on the side.