Remove any discolored leaves and the small leaves at base of each artichoke; trim stem even with base. Cutting straight across, slice 1 inch off top and discard. Snip off points of remaining leaves with sissors. Rinse artichokes under cold running water. Combine oil, onion, garlic, salt, savory, and thyme in Dutch oven. Place artichokes upright in Dutch oven; pour wine oven artichokes. Heat to boiling; reduce heat. Cover and simmer until bottoms of artichokes are tender when pierced with knife, about 1 hour. Remove artichokes carefully from Dutch oven with tongs or 2 large spoons. Place upright on individual serving plates. Accompany each serving with small cup of wine liquid for dipping leaves.