Trim the outer leaves of each artichoke and the stem to 2 inches long. Using a peeler, peel the stems of each artichoke. In a bowl, combine the artichokes and juice from the lemons. Cover with ice water and allow to sit for 2 hours. Drain well. Using your hands, flatten each artichoke to the shape of a flower.
In a large earthenware pan, over medium heat, add the olive oil. Add the artichokes, side by side and stem up. Cook the artichokes until tender, turning the artichokes several times for overall browning. Using a wooden spoon, press each artichoke firmly to the bottom of the pan so that the leaves flatten out. Continue to cook for 10 minutes.
Carefully sprinkle a little water over the artichokes, this will crisp the artichokes. Continue to cook for 2 minutes.
Place the artichokes on a large platter and serve. Garnish with grated Pecorino Romano.