Grate the zest of 2 of the lemons and reserve. Squeeze the juice from 1 of the zested lemons into a large bowl filled halfway with cool water. Set aside. Juice the remaining 3 lemons and reserve the juice. Cut the stems off of the artichokes so that they will stand upright. Remove any tough or blemished outer leaves and, using a sharp knife, cut off the top 1/4 of the artichoke. Using kitchen shears, cut the thorns from the tips of the remaining leaves. Using your fingers, gently pry the leaves apart to reveal the inner choke and, using a spoon or a melon baller, scoop out some of the inner leaves and the fuzzy choke and discard. This should leave a sizable cavity in the center of each artichoke for stuffing. Repeat with the remaining artichokes, transferring artichokes to the acidulated water as soon as they are trimmed and cleaned.
In a medium mixing bowl, combine the bread crumbs, reserved lemon zest, Pecorino Romano, garlic, parsley, mint, 6 tablespoons of the reserved lemon juice, and 1 cup plus 2 tablespoons of the olive oil. Add 1/2 cup plus 1 tablespoon of warm water and mix thoroughly. The crumb stuffing should be moist enough to clump together when pinched between your fingers. Season, to taste, with salt and freshly ground black pepper. Working 1 at a time, remove the artichokes from the lemon water and invert to drain thoroughly. Using a small spoon, fill the cavities of the artichokes with the stuffing, pressing downward as you add the stuffing. You should have enough stuffing to fill all 6 cavities of the artichokes as well as stuff some of the large outer leaves. Drizzle each artichoke with 1 tablespoon of the remaining olive oil.
In a wide saucepan large enough to hold the artichokes in 1 layer, place the artichokes, stem side down and stuffing up, and add about 1-inch of cold water; it should come up to the bottom of where the leaves begin. Add any remaining lemon juice and the remaining olive oil. Cover the pot and bring the liquid to a boil, reduce the heat to a simmer, and continue to cook, covered, until the leaves pull away easily from the artichokes and the heart is tender when pierced with the tip of a knife, 35 to 40 minutes. Carefully remove the artichokes from the pot and set aside to cool slightly. Serve the artichokes either warm or at room temperature.