Green Chile Cheeseburgers

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2 pounds ground chuck, 80 percent to 85 percent lean

1 teaspoon kosher salt

1 teaspoon freshly ground black pepper

8 thin slices Chihuahua or provolone

4 good-quality hamburger buns, toasted

Green Chili Sauce, recipe follows

Romaine lettuce leaves, optional

4 thick slices beefsteak tomatoes, optional

Pickled jalapenos, optional

Green Chile Sauce:

2 poblano chiles, grilled, peeled, seeded, and chopped

1 medium white onion, grilled and chopped

1 to 2 cloves garlic, chopped

2 tablespoons chopped fresh epazote, or fresh oregano leaves

1/4 cup cold water

1 tablespoon honey

1/4 teaspoon kosher salt

1/4 teaspoon freshly ground black pepper