Pollo a la Brasa (Peruvian Grill-Roasted Chicken)

 Whisk ½ cup beer, garlic, lime juice, soy sauce, salt, mustard, pepper, thyme, and cumin together in liquid measuring cup. Refrigerate remaining beer, still in can, until ready to grill. Using your fingers or handle of wooden spoon, gently loosen skin covering chicken breast and leg quarters. Using paring knife, poke 10 to 15 holes in fat deposits on skin of back. Tuck wingtips underneath chicken.

 Place chicken in bowl with cavity end facing up. Slowly pour marinade between skin and meat and rub marinade inside cavity, outside skin, and under skin to distribute. Cover and refrigerate for 24 hours, turning chicken halfway through marinating.

 Using large piece of heavy-duty aluminum foil, wrap wood chips in 8 by 4½-inch foil packet. (Make sure chips do not poke holes in packet.) Cut 2 evenly spaced 2-inch slits in top of packet.

 Place beer can in large, shallow bowl. Spray can all over with vegetable oil spray. Slide chicken over can so drumsticks reach down to bottom of can and chicken stands upright; set aside at room temperature while preparing grill.

FOR A CHARCOAL GRILL: Open bottom vent fully and place disposable pan in center of grill. Light large chimney starter two-thirds filled with charcoal briquettes (4 quarts). When top coals are partially covered with ash, pour into 2 even piles on either side of disposable pan. Place wood chip packet on 1 pile of coals. Set cooking grate in place, cover, and open lid vent fully. Heat grill until hot and wood chips are smoking, about 5 minutes.

FOR A GAS GRILL: Remove cooking grate and place wood chip packet directly on one of outside burners. Set grate in place; turn all burners to high; cover; and heat grill until hot and wood chips are smoking, about 15 minutes. Turn 2 outside burners to medium and turn off center burner. (Adjust outside burners as needed to maintain grill temperature between 350 and 375 degrees.)

 Scrape cooking grate clean with grill brush. Transfer chicken with can to center of cooking grate with wings facing piles of coals (or outer burners on gas grill) at 3 and 9 o’clock (ends of drumsticks should rest on grate to help steady bird). Cover grill (with top vent open for charcoal grill) and cook for 15 minutes. Using tongs and wad of paper towels, rotate chicken 90 degrees so wings are at 6 and 12 o’clock. Continue cooking and turning chicken at 15-minute intervals until thickest part of thigh registers 170 to 175 degrees, 1 hour to 1¼ hours longer.

 With large wad of paper towels in each hand, transfer chicken and can to clean bowl, keeping can upright; let rest for 15 minutes (do not discard paper towels). Using wads of paper towels, carefully lift chicken off can and onto cutting board. Discard can. Carve chicken, transfer to platter, and serve.