Trim the artichokes as directed for Roman-style artichokes, but cut off the stem leaving only a short stump. As you remove outer leaves, keep them longer at the base and trim tough tops. Rub cut parts with juice from the 1/2 lemon to prevent darkening.

Turn bottoms up, gently spread leaves, and press against a work surface to flatten without cracking. Turn right side up and season with salt and pepper.

Use a deep skillet or saute pan and add oil to come 1 1/2 inches up the side (3.8 cm). Heat to medium and slip in artichokes bottoms up. Cook about 5 minutes, turn over, then turn from time to time. Cook until the thick bottom is tender when pierced with a fork (about 15 minutes or longer). Regulate heat so the oil does not overheat.

Transfer artichokes bottoms up to a surface and press further with a wooden spoon or spatula.

Turn heat under the pan to high. Keep a bowl of cold water nearby. When oil is very hot, slip artichokes in bottoms up. Fry a few minutes, turn them over, then sprinkle with cold water (stand back because oil will spatter).

When oil stops sputtering, drain face down on towels or a rack. Serve leaves up.