Preheat the oven to 400°F.
Prep the vegetables. Cut the red onion into wedges and slice the Anaheim chilis lengthwise, removing the seeds. Place them on a sheet pan with the peeled garlic clove. Sprinkle everything with salt and drizzle with olive oil.
Roast the vegetables. Roast in the oven for about 15–20 minutes, or until the vegetables are softened and starting to brown. Roasting brings out their natural sweetness and smoky flavor.
Make the green chili mixture. Once roasted, add the onion, chilis, and garlic to a blender or food processor. Add ½ teaspoon of salt and the juice of one lime. Pulse until the mixture is well combined but still chunky—think rustic salsa, not smooth sauce.
Grill the burgers. Preheat your grill over medium-high heat. Season your beef patties with salt and pepper. Grill the burgers for about 3–5 minutes per side or until they reach your preferred doneness.
Let the burgers rest. Once cooked, remove the patties from the grill and let them rest for 5–10 minutes to allow the juices to redistribute.
Assemble your burgers. Start with your bun or lettuce wrap, then layer on the burger patty, Monterey Jack cheese (if using), and a generous spoonful of the roasted Anaheim chili mixture. Serve hot!