Artichokes are great any way you eat them — shaved when raw with a heavy dose of olive oil and cheese, steamed with the tender leaves dipped into a lemony-basil dressing of sorts, or grilled during the warmer months.
Peel off the outer layers of the artichokes until you reach the tender leaves. Prepare a bowl of water and then squeeze the juice of the 2 lemons in it. Cut the artichokes in half and remove any fuzzy bits in the middle, placing them immediately in the lemon water. Either slice the artichokes thinly or shave on a mandoline into a bowl.
Dress the artichokes with the remaining ingredients, adding more cheese or salt and pepper as needed.