Peruvian Chicken with Green Sauce (Pollo a la Brasa with Ají Verde)

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One 12-ounce bottle beer (lager)

3 tablespoons soy sauce

1 tablespoon ground cumin

1 tablespoon hoisin sauce

1 tablespoon chopped fresh oregano

1 tablespoon freshly ground black pepper

1 tablespoon white vinegar

1/2 tablespoon chopped fresh rosemary

1/2 tablespoon kosher salt

3 cloves garlic

Juice of 1/2 lime

One 3- to 4-pound chicken

Ají Verde (Green Sauce), for serving, recipe follows

Ají Verde (Green Sauce):

1/2 cup huacatay (black mint paste)

1/2 cup mayonnaise

3 tablespoons olive oil

1 tablespoon lime juice

2 cloves garlic

1 bunch fresh cilantro

1/2 red onion

1/4 jalapeño

Kosher salt