To clean the artichokes peel off the outer tough green leaves. With a sharp knife cut across the top of the artichoke about a 1/2-inch to remove the sharp spines. With a long narrow spoon scoop out the center choke of the artichoke. With a small knife or a vegetable peeler, pare down the outside dark green exterior of the base and stem. Place in acidulated water and repeat process with other artichokes.
Drain artichokes well. Put oil in a tall pot and over medium heat fry the artichokes until they are slightly golden in color. Remove artichokes from oil and drain on paper towels. Turn temperature of oil up to medium high. Return artichokes to the oil and fry until they are completely opened and deep golden brown. Remove from oil, place face down on paper towels to let all the oil drain.
Season with salt and pepper garnish with parsley leaves and serve warm with the aioli.
Meyer Lemon Aioli:
In a mortar, pound the garlic and salt to form a paste. Stir in the egg yolk, lemon zest, and juice until integrated. Add the olive oil in a slow trickle to the side of the mortar until completely combined.