Process all ingredients except for the chicken in a blender or food processor until a smooth paste forms, 10 to 20 seconds. Using fingers loosen skin over thighs and breast and remove any excess fat. Rub half of the paste beneath skin of chicken. Spread entire exterior surface of chicken with remaining paste. Tuck wingtips underneath chicken. Place chicken in a gallon-size zipper bag and refrigerate at least 6 hours or up to 24 hours.
Adjust oven rack to lowest position and heat oven to 325 degrees F. Place vertical roaster or can of beer in a baking pan. Slide chicken onto vertical roaster or beer can. Roast until skin just begins to turn golden and instant-read thermometer inserted into thickest part of the breast registers 140 degrees F., 45 to 55 minutes. Carefully remove chicken and pan from oven and increase oven temperature to 500 degrees F.
When oven is heated to 500 degrees F., place 1 cup of water in bottom of roasting pan and return to oven. Roast until entire skin is browned and crisp and thermometer registers 160 degrees F. inserted into the breast and 175 degrees F. in the thickest part of the thigh, about 20 minutes (replenishing water as necessary, to keep pan from smoking) rotating bird 180 degrees halfway through cooking.
Carefully remove chicken from oven and lest rest, still on vertical roaster or can, 20 minutes. Carve chicken and serve with Spicy Mayonnaise.