Pre-heat a cast iron grill to high.
Prepare a court bouillon to poach the artichokes: Fill a large pot 3/4 full with water. Add bay leaves, thyme, red pepper flakes and salt. Bring to a simmer.
Prepare artichokes. Remove tough outer leaves of the artichokes and trim stems. Use a vegetable peeler to remove tough outer green layer from stem. Cut off the top 1/3 of the head to remove tough ends of the leaves. Rub with lemon as you work so they dont turn brown.
Add artichokes to the court bouillion and simmer for 8-10 minutes. Stir occasionally so the artichokes cook evenly. Remove, allow to cool then cut in half down the middle through the stem.
Mix together olive oil with minced garlic, salt and pepper. Lay artichoke halves cut-side up in a roasting dish and drizzle with olive oil mixture. Place artichokes on grill and mark off 2-3 minutes per side.
To serve, drizzle with a little balsamic, top with grated parmesan and garnish with chopped parsley.