Prepare artichokes. Remove the tough outer leaves of the artichokes and trim the stems. Use a vegetable peeler to remove the tough outer green layer from the stem. Cut off the top third of the head to remove the tough ends of the leaves, then split it down the middle. Rub with lemon as you work so they don't turn brown.
Mix together the olive oil, balsamic vinegar, salt, pepper and garlic. Lay the artichoke halves cut-side up in a roasting dish and drizzle with the olive oil mixture. Roast in the oven until the artichokes are tender, about 20 minutes.
To serve, top with the cheese and garnish with the parsley.