In a 5- to 6-quart pan, combine broth, vinegar, wine, bay leaves, thyme, salt, and 1 cup water.
Break off artichoke leaves down to fleshy bottoms (save leaves to cook for other uses, if desired). With a vegetable peeler or knife, trim fibers from artichoke bottoms and trim stem ends; with a spoon, scrape out and discard fuzzy centers. Rinse artichoke bottoms and add to pan. Bring to a boil over high heat; reduce heat, cover, and simmer for 15 minutes.
As artichokes cook, rinse fennel and trim off stalks 1 to 2 inches above heads. Reserve feathery green leaves; discard stalks. Trim discolored spots, coarse fibers, and root ends from heads. Cut heads in half vertically.
Trim root ends and coarse tops from leeks; peel 1 layer off each leek. From green end, cut each leek in half lengthwise just down to white part. Rinse under running water, flipping green ends.
Trim tops off celery stalks to make head 8 to 9 inches long. Rinse.
Lay fennel, leeks, and celery over artichokes in pan (liquid does not cover). Cover pan and simmer until vegetables are just tender when pierced, 15 to 20 minutes longer. Let cool, covered, at least 1 hour. Lift out the vegetables.
Boil cooking liquid over high heat, uncovered, until reduced to 3/4 cup, about 15 minutes. Pour through a strainer into a glass measure; discard residue. If needed, add water. Return liquid to pan, add cream, and bring to a boil over high heat. Remove from heat.
Slice vegetables vertically into 4 or 8 equal portions each (or cut thinner if desired). Arrange vegetables equally on plates, moisten with dressing, drape with anchovies, and sprinkle evenly with eggs. Chop some of the reserved green fennel leaves and use to garnish salads.
Note: Nutritional analysis is per main-dish serving