Add water to the pressure cooker. Add all but 3 tablespoons of lemon juice, salt, and bay leaf. Mix until the salt dissolves. Place reserved lemon rinds in water.
Trim the artichokes: Cut off the stems. Tear off and discard top 2-3 layers of tough leaves. From the top of the artichoke, cut off 1-1 1/2 inches. Carefully expose inner leaves and choke. Pull out and discard any thorny leaves. Scoop out any fuzzy matter from center of choke. Dampen whole surface of artichoke in the lemon water and place artichokes upside down in the pressure cooker.
Cover and set to high pressure for 7 minutes.
Release the pressure using the quick-release method.
Unlock and remove lid. Carefully remove artichokes from pressure cooker using a slotted spoon. Cool to room temperature.
Mix mayonnaise, the rest of the lemon juice, garlic, and Tabasco to taste.
Carefully open the center of each artichoke. Fill with 1/4 of lemon mayonnaise. Sprinkle top with parsley or dill.
Recipe courtesy of Deni, Reprinted with permission.