Add artichokes, garlic, and enough water to cover them to a large pot. Bring the water to a boil and cook until the choke is just tender. For large artichokes, about 20-25 minutes. You can place a heat-proof plate on top of the artichokes to keep them submerged. As this traps heat, we would suggest reducing the cooking time by 5-10 minutes. See note on cooking time above.
Lift each artichoke from the water upside down to allow water to drain off back into the pot and allow it to cool so you can handle them.
Cut each artichoke in half vertically, such that the stem and artichoke are both cut in half.
Scoop out the fuzzy choke and the very small center spiky leaves with a spoon. If the artichoke is cooked enough, this should be very easy to remove. Cover until you’re ready to grill.
When you are ready to grill, drizzle the artichokes generously with olive oil, salt, and pepper. Place each artichoke cut-side down on the grill and cook for about 2-3 minutes. Flip and cook for a remaining 2-3 minutes or until you have some grill marks.
Serve with aioli or homemade mayonnaise for dipping.