Artichokes: Squeeze juice from 2 lemon halves into a large bowl; add lemon halves. Fill bowl with water.
To prepare an artichoke for cooking, first cut off the stem. Starting at the base of the artichoke, bend the tough dark green outer leaves back and snap them off where they break naturally: continue until all of the outer leaves have been removed, leaving a cone of tender pale green leaves. Using a small sharp knife, trim the outside edge of the base of the artichoke until it is smooth. Rub the trimmed edge with 1 of the remaining lemon halves. Cut artichoke lengthwise into quarters.
Rub the cut sides of these quarters with lemon to prevent any discoloration. Using the small knife, carefully cut out the hairy choke and the spiky purple-tipped leaves from each artichoke quarter. Rub each cut area with lemon. Trim the tougher leaf tops from each quarter so that all that remains is the choicest, most tender portion of the artichoke. Cut quarter into two wedges. Places wedges into the lemon water. Repeat with the remaining artichokes.
Bring the chicken broth, olive oil and bay leaf to a boil in a heavy large pot (do not use aluminum or cast iron). Drain artichokes; add to pot. Return to boil. Reduce heat to medium-low; simmer until artichokes are tender, about 20 minutes. Using slotted spoon, transfer artichokes to medium bowl. Reserve 1 cup cooking liquid in small bowl.
Stew: Place potatoes, salt, bay leaf, 1/2 tsp mustard seeds and celery seeds in large saucepan. Pour in enough cold water to cover potatoes generously. Boil until potatoes are tender, about 20 minutes. Drain. Cool 15 minutes; peel. Stir saffron in heavy large pot over medium-low heat until fragrant, about 2 minutes. Add reserved 1 cup cooking liquid; bring to simmer. Add artichokes, potatoes, mussels, shallots, butter and 3/4 tsp mustard seeds. Bring to boil. Cover pot; cook until mussels open and potatoes are golden, about 8 minutes. (Discard any unopened mussels.) Mix in green onions. Season with salt and pepper. Sprinkle with chives and serve.Servings: 6