Preparing the Chicken: Rinse the chicken with cold water. Pat completely dry with paper towels. Trim excess fat and skin from the opening. Place the chicken breast side up on the work surface. Pull one leg away from the body of the chicken and, with a sharp knife, cut through the skin between the leg and the breast until you hit a joint. Do not cut through the joint. With your fingers behind the joint, bend the leg back until the joint pops. Repeat with the other leg. Lift the breast to open the cavity and reveal the small ribs. Cut through the rib bones (starting from the thigh) on both sides of the breast up to, but not through, the shoulder joints. Turn the chicken so that it lies skin side up on the work surface. Press firmly in the center of the breast with the heel of your hand to crack the breastbone, flattening the breast to the same thickness as the legs and back.
Preparing the Adobo: Using a mortar and pestle, mash the garlic to a paste with the ají molido, salt, black pepper, oregano, cumin, and allspice. Add the olive oil and stir to mix.
Seasoning the Chicken: Using the lemon slices, scoop up some of the seasoning mixture and rub it all over the chicken. Using your fingers or a small paring knife, loosen the skin around the breast and thighs and insert the lemon slices and remaining mixture to intensify the flavors. Cover the chicken with plastic wrap and refrigerate, preferably overnight, before grilling or broiling. When ready to proceed, scrape the excess marinade from the chicken and place it in a bowl with some olive oil for basting.
To Grill: Prepare the grill with hardwood charcoal and start the fire. When the flames have subsided but some of the coals are still fiery red, place the chicken on the grill and cook for 5 minutes on each side. Move the chicken to a cooler section of the grill and wait until the coals become ashy. Baste with the reserved marinade-oil mixture and grill until tender and browned on both sides, about 20 minutes, turning occasionally with tongs. If you have a grill fitted with a lid, leave the cover on, with the smoke vent slightly open.
To Broil: Place the chicken on a baking sheet and slide it into a preheated broiler about 4 inches from the heat source. Broil for 20 minutes on each side, starting with the skin side down. Baste with the reserved marinade-oil mixture and finish broiling for an additional 5 minutes, skin side up, until the chicken is golden brown.
Serving: Transfer the chicken to a cutting board and cut into serving pieces. Slice the breast and drizzle with some of the pan juices if broiling.