In a large saucepan, bring the split peas and broth to a boil over moderate heat. Cover and boil gently until the peas are tender, about 45 minutes. Add all the remaining ingredients to the saucepan, cover and boil gently until the vegetables are very tender, about 45 minutes longer. Pick out and discard the thyme sprigs. Puree the soup in batches in a food mill, food processor or blender. Season with additional allspice, salt and pepper and serve hot. (The soup can be refrigerated for up to 5 days or frozen for several weeks. Stir well after reheating.) soup 72