Fill a large pot (a stock pot works well) with cold water; roll the 2 lemons on the counter with your palm to"loosen" juices, then cut in half and squeeze the juice into the pot of water and toss in the squeezed lemon halves and the smashed garlic.
Trim the artichokes: cut off the top quarter from the artichokes and discard, remove the bottom and tough outer layer of stem, snap off the tough outer leaves from the base, remove dark green areas of the base.
Cut artichokes in quarters and remove the choke and small purple leaves.
Add trimmed and quartered artichokes to the pot of water, cover, and simmer over medium heat until tender, about 45 minutes; drain and set aside to let cool.
In a large bowl, combine the lemon juice, parsley, basil, mint, minced garlic, lemon peel, capers, cubed bread, and tomatoes, tossing to coat; season to taste with salt and pepper.
Get two large serving platters and arrange the cooked and cooled artichokes cut-side-up.
Place a spoonful of the tomato stuffing in the middle of each artichoke quarter, drizzle with olive oil, garnish with the parsley sprigs, and serve.