Trim the stem of an artichoke so the base is flat and even. Trim the top inch off the artichoke and remove and discard any tough, woody outer leaves. Gently open up the leaves to get to the center. Using a spoon, scoop out the fuzzy choke in the center. Using scissors, trim off the sharp points of the large outer leaves. Rub and pour lemon juice all over the inside and outside (reserve half of the juice). Repeat with remaining artichokes.
Mix together pulverized crackers, Pecorino, olive oil, parsley, Italian seasoning, garlic, lemon zest and salt and pepper.
Pack each artichoke with the stuffing mixture, starting with the interior and working your way around between the outer leaves. Continue this process with the remaining artichokes. Place artichokes in an 8-inch square baking dish and add about 1 inch of chicken stock and the reserved lemon juice to the bottom of the dish. Cover tightly with foil.
Bake until leaves pull out easily and the meat at the bottom of the leaves is tender, 1 hour to 1 hour 30 minutes. Preheat the broiler. Take off foil, drizzle the artichokes with olive oil and broil until tops are golden brown, about 5 minutes. Serve!