In large Dutch oven or deep skillet, combine 3 cups (750 mL) water, vinegar, celery, carrots, parsley, cloves, onion, bay leaves, peppercorns and sa< bring to boil. Reduce heat, cover and simmer for 10 minutes.
Meanwhile, using kitchen shears, cut along both sides of backbone of each hen and remove backbone. Add hens to liquid, skin side up and in single layer; bring to simmer over high heat. Reduce heat, cover and simmer for 25 minutes. Remove from heat; let stand, covered, for 10 minutes. Remove hens from pan. Strain liquid, reserving 1-1/3 cups (325 mL). (Make-ahead: Let hens and liquid cool for 30 minutes; refrigerate until cold. Cover and refrigerate separately for up to 24 hours.)
Place hens on broiler pan, skin side up; brush with oil. Broil 6 inches (15 cm) from heat until browned, about 8 minutes.
Meanwhile, in saucepan, boil reserved liquid until reduced to 1/3 cup (75 mL); remove from heat and whisk in butter. Serve with hens.