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1
Whisk beer, teriyaki sauce, chili powder, and garlic powder together in a bowl; pour into a resealable plastic bag. Add the chicken, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator 6 to 24 hours.
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2
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
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3
Remove chicken from the marinade and shake off excess. Discard the remaining marinade.
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4
Cook the chicken breasts on preheated grill until no longer pink in the center and the juices run clear, 7 to 10 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Arrange chicken breasts in a baking dish and top each with a slice of Muenster cheese.
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5
Preheat oven to 350 degrees F (175 degrees C).
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6
Combine tomatillos and water in a large saucepan; bring water to a boil, place cover on saucepan, reduce heat to medium-low, and cook until tomatillos begin to burst, 7 to 10 minutes. Stir onion and garlic into tomatillo sauce; season with salt and pepper; continue cooking at a low boil until onion is tender, about 15 minutes.
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7
Pour tomatillo sauce into a blender. Cover and hold lid down; pulse a few times before leaving on to blend until smooth. Stir sour cream and cilantro into the tomatillo sauce; pour over the chicken and Muenster cheese.
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8
Bake in preheated oven until cheese melts, about 15 minutes.
