Notes: If making up to 1 day ahead, cover and chill. Bring to room temperature to serve.
Pour about 3 quarts water into a 6- to 8-quart pan. Add 3 tablespoons vinegar, 1 teaspoon olive oil, cumin seed, and peppercorns. Cover and bring to a boil over high heat.
Meanwhile, slice off and discard about 1 inch from tops of artichokes. Pull off and discard small outer leaves from bases of artichokes. With scissors, cut off and discard remaining thorny tips from outer leaves. Trim and discard discolored stem ends, and peel stems. Cut artichokes in half lengthwise and rinse well.
Add the artichokes to boiling water. Return to a boil, cover, and simmer until the artichoke bottoms are tender when pierced with a fork, 14 to 18 minutes.
With a slotted spoon, lift artichokes from pan and set on a rimmed plate. Pour cooking liquid through a strainer into a deep bowl. Reserve spice mixture; discard all but 1 1/3 cups of the cooking liquid.
Add spice mixture, 1/3 cup vinegar, 2 tablespoons olive oil, onion, tarragon, mustard, and garlic to cooking liquid in bowl.
If desired, scoop out and discard fuzzy artichoke centers. Add artichokes to bowl; mix to coat well, and add salt to taste. Turn occasionally for at least 30 minutes, or cover and chill up to 1 day, turning occasionally.