Pollo en Pipian Verde

Rinse chicken and cut garlic head in half crosswise. In a 6-quart kettle cover chicken, garlic halves, onion, coriander, salt, peppercorns, and allspice with water and simmer, covered, 1 hour, or until chicken is tender. Transfer chicken to a bowl to cool and reserve stock. Shred chicken, discarding skin and bones. Pour reserved stock through a fine sieve into a bowl, pressing garlic pulp through sieve. Measure 3 cups stock for sauce and reserve remainder for another use. Chicken and stock may be made 1 day ahead and cooled completely, uncovered, before being chilled separately, covered. (Stock keeps, frozen, 1 month.)