Squeeze the juice from the lemon halves into a large pot of cold water; add the squeezed lemon halves and the whole garlic. Cut off the top quarter of each artichoke and discard. Use a small sharp knife to trim the stem of the artichokes. Starting at the base, bend the tough outer leaves back and snap off where they break naturally, leaving the tender inner leaves. Trim the outside of the base until no dark green areas remain. Cut the artichokes in half and then into quarters. Cut out the fibrous choke and small purple-tipped leaves. Submerge the artichoke quarters in the lemon water. Cover and boil until the artichokes are tender, about 45 minutes. Drain. Set the artichoke quarters aside to cool to room temperature.
Mix together lemon juice, herbs, garlic, lemon peel, capers, bread, and tomatoes in a large bowl. Season with salt and pepper, to taste.
Arrange artichokes, cut side up, on 2 platters. Spoon the tomato mixture into the center of the artichoke quarters, dividing equally. Drizzle with olive oil. Garnish with the parsley sprigs and serve.