Grilled Salsa Verde Chicken

Name: Grilled Salsa Verde Chicken
Prep time: 20 min
Total time: 20 min
Cuisine: Mexican, Latin American, American
Ingredients: 1 jar salsa verde, divided; 2 tbsp. extra-virgin olive oil; Juice of 1/2 a lime; 2 cloves garlic, minced; 1/2 tsp. chili powder; 1/2 tsp. ground cumin; 1 lb. boneless skinless chicken breasts; 4 slices Monterey jack; 1 jalapeño, thinly sliced; 1/2 red onion, finely chopped; 2 tbsp. freshly chopped cilantro; Lime wedges, for serving