Trim the artichokes for eating by cutting off the ends of the stalks and the sharp tips of the leaves.
Boil one inch of water in a large pot with a steamer insert. Add the artichokes to the pot, put the lid on, and steam for 40 minutes, or until a leaf can be easily removed.
Cut the artichokes in half, vertically, and remove the choke. Season with salt and pepper.
Brush with olive oil and sear on both sides on a hot grill pan or large skillet.
For the Roasted Garlic Aioli:
Preheat your oven to 400°.
In a small ceramic ramekin, place 2 tablespoons of olive oil and the garlic. Cover tightly and bake for one hour.
When the garlic is tender, add it to a food processor, with the mayonnaise, pepper, and lemon juice. Chop it all up, and with the motor running drizzle in 1 tablespoon of olive oil.