Step 1Snap off outer leaves of artichokes and trim tops and bottoms according to preparation instructions. Place artichokes in bowl with juice of 1 lemon and enough water to cover. (If using larger artichokes, trim and quarter them, then remove chokes.) When all are done, drop them into pan of boiling water with juice of second lemon and simmer until tender-firm, about 10 minutes. Drain. Just before sauteing, slice them lengthwise in half or thirds. (If using larger artichokes, parboil quarters, then thinly slice them.)
Step 2Chop parsely with garlic and zest; set aside.
Step 3Heat oil in large skillet over fairly high heat. Add artichokes and saute until they begin to color in places, after several minutes. Add green onions and wine. When wine boils off, 2 to 3 minutes, add 1 cup water or chicken broth and half parsley mixture and tarragon. Lower heat and simmer until artichokes are fully tender, about 5 minutes, then add rest of herbs and season with salt and pepper. Tip artichokes, with their juices, onto serving plate.