Shortly before cooking, rotate each baby artichoke against the blade of a very sharp stainless steel paring knife to trim off the outermost layer of leaves. Cut off the stems level with the bottom of the artichoke, and cut off and discard the top half. Toss in lemon juice to keep them from darkening.
Put the trimmed artichokes in a nonaluminum pot with enough cold water to cover them by about 1-inch. Place a small plate directly on the artichokes -- in the pan -- to keep them submerged. Bring to a simmer over high heat. Turn the heat to low and keep the artichokes at a bare simmer for about 15 minutes.
Meanwhile, make the vinaigrette. Combine the garlic, lemon juice and parsley. Whisk in oil. Season with salt and pepper.
Poke the artichokes with a paring knife to test for doneness. Should feel like a slightly underdone boiled potato. When done, drain and pour vinaigrette over them.