Clean the artichokes and carefully remove the tough outer leaves.
In a medium stock pot, bring 6 cups water and 1 cut lemon (rough wedges are fine) to a boil.
Using a peeler, peel the stem and shape the outside of the heart.
Cut the artichoke in half, from tip to stem, exposing the thistle but not removing it.
Use half of a cut lemon to coat the artichokes at every step to prevent oxidation (this happens almost instantly).
Boil the artichokes in boiling water with the lemons for 10 to 15 minutes. Use a paring knife in the thickest part of the heart to check doneness. (You’ll want to feel that the knife enters and exits very easily.)
Carefully remove the artichokes from the pot, let them drain and cool, and cut the side down on a paper towel.
Once cool enough to handle, use a small spoon to remove the thistle from each artichoke half carefully. They should come out easily now that they’re fully cooked.
Once cleaned, the artichokes can be kept covered in the fridge for a few hours or overnight.
When ready to serve, turn the artichokes cut side up, drizzle with olive oil and season with salt and pepper.
Brown artichokes under the grill/broiler, on a hot barbecue or in a hot skillet.
Once browned and warmed through, remove them from the heat and plate them cut-side up.
Season them with fresh lemon juice and top with plenty of garlic aioli, Parmesan shavings, capers, and parsley.