Add water, Worcestershire sauce, garlic, bay leaves, onion, salt, sugar, pepper, paprika, and allspice. Cover and simmer 1 1/2 hours.
Remove bay leaves and garlic clove.
Add carrots and celery. Cover and cook 30 to 40 minutes longer. To thicken gravy, remove 2 cups hot liquid. Using a separate bowl, combine 1/4 cup water and cornstarch until smooth.
Mix with a little hot liquid and return mixture to pot. Stir and cook until bubbly.