Place onion, garlic, cilantro, salt, and garlic powder in a food processor or blender and process until finely chopped. Add the tomatoes, tomatoes and chilies, and lime juice and pulse several times until blended but chunky. Allow to sit at room temperature for 30 minutes to let the flavors mingle. Any leftover salsa can be stored, covered, in the refrigerator for up to 2 weeks.

Prepare the grill for direct and indirect heat and preheat to medium. Oil the grates.

Place the peppers over direct heat and grill for 10-15 minutes, flipping often, until charred. Place in a bowl and cover with a plate or plastic wrap and let steam until cool enough to handle. Peel the peppers, slit each one from stem to tip, and scrape out the seeds.

Stuff each pepper with the cheese. Place a large piece of heavy-duty foil over indirect heat, place the peppers on top and grill until the cheese is fully melted, 6-8 minutes.

Serve with the salsa.