Bring beans and soaking water to full boil in large saucepan. Boil 2 minutes; cover, remove from heat, and stand 60 minutes. Drain and rinse.
Heat oven to 325°F. Heat oil in covered 6-quart oven-safe pot over medium. Cook onion, carrots, and celery 7 minutes, then garlic 1 minute.
Add drained beans, broth, bay, savory, and pepper. Simmer; cover tightly and transfer to oven.
Bake 1 1/2 hours; stir gently and check a bean. Bake covered another 30 to 45 minutes until nearly tender, adding measured hot water if liquid no longer covers beans.
Fold in ham; bake covered 15 to 20 minutes more until beans tender and ham 165°F. Add remaining optional water only if too thick.
Discard bay; stir in vinegar. Taste before adding up to measured 1/4 teaspoon salt. Rest 5 minutes; divide among six bowls.