To prepare the stew, combine 3 cups water and 1/3 cup lemon juice in a large bowl. Working with 1 artichoke at a time, cut off the stem to within 1 inch of base, and peel stem. Remove the bottom leaves and tough outer leaves, and trim about 2 inches from the top of the artichoke. Cut artichoke in half vertically. Remove fuzzy thistle from bottom with a spoon. Trim any remaining leaves and dark green layer from base. Rub edges with a lemon half; place the artichoke halves in lemon water. Repeat procedure with remaining artichokes.
Heat a Dutch oven over medium-high heat, and add veal, browning on all sides. Add onion, and cook for 5 minutes. Add the wine and 1 can of broth; bring to a boil. Cover, reduce heat, and simmer 45 minutes.
Drain the artichoke halves. Add artichoke halves, 1 cup water, 1/3 cup lemon juice, 1/2 cup dill, 1 can of broth, salt, and pepper to pan; cover and simmer for 30 minutes or until the artichokes are tender. Remove veal and artichoke halves with a slotted spoon. Keep warm.
To prepare avgolemono, combine the egg, 3 tablespoons water, and 2 tablespoons lemon juice in a medium bowl. Combine 2 tablespoons water and the cornstarch in a small bowl; add to the egg mixture. Add the egg mixture to juices in pan. Bring to a boil, and cook 5 minutes, stirring constantly with a whisk. Serve the sauce over the veal and artichokes, and sprinkle with 1/4 cup dill. Garnish with lemon wedges, if desired.