Green Chile Cheeseburger

Name: Green Chile Cheeseburger
Ingredients: 2 pounds Angus-quality ground beef; 2 tablespoons kosher salt; 1 tablespoon fresh ground black pepper; 4 pounds mild green chiles, (recommended: New Mexico Hatch Chiles); 2 pounds hot green chiles, (recommended: New Mexico Hatch Chiles); 3 large white onions, peeled; 6 garlic cloves, peeled; 1 tablespoon fresh epazote; 1/2 tablespoon dried Mexican oregano; 1/2 cup grapeseed oil; 1 cup water; Oil, for brushing grill; 4 hamburger buns; 1 pound Asadero cheese, sliced 1/4-inch thick; 1 pound mozzarella cheese, sliced 1/4-inch thick