Begin by trimming each artichoke's base and top third of leaves with a serrated knife. Remove the bottom two layers of tough outer leaves.
With a pair of kitchen scissors, trim the sharp tips of the remaining leaves. Rub lemon wherever cuts have been made and set aside.
Place artichoke on a large sheet of aluminum foil stem side down. Tuck slivers of garlic between leaves, and dress with a generous two to three tablespoons of olive oil, a squeeze of lemon juice, and a pinch of salt.
Wrap foil around the artichoke.
Place wrapped artichokes in a snug pan, and bake for one hour and 20 minutes.
Remove artichokes from oven and allow to slightly cool before unwrapping foil.
Combine egg, mustard, lemon juice, zest, and garlic in a small food processor/blender and process to combine. Slowly stream in oil until mixture thickens to a mayonnaise like consistency. Season with salt.
Enjoy your artichoke by removing outer leaves one by one, dipping them in aioli.
Once the larger outer leaves have been removed and consumed, use a teaspoon to remove the fuzzy choke covering the heart, and discard. Eat the buttery artichoke heart with more aioli.