Fill a large bowl with water. Squeeze the juice from 1 lemon into the water.
Working with 1 artichoke at a time, remove tough outer leaves to expose the light yellow core. Peel the stem end of the artichoke, keeping about 1 inch of the stem intact and exposing the pale, tender core. Trim 1 inch off the top and cut the artichoke in half lengthwise through the center. Using the tip of a spoon, scoop out the furry choke. Add the cleaned artichoke halves to the lemon water. Keep the artichokes in the water until ready to cook. Just before cooking, spread the artichokes on paper towels, sliced side down, to drain and thoroughly pat dry.
In a large sauté pan over medium-high heat, warm olive oil until nearly smoking. Sprinkle the pan generously with salt and pepper. Carefully place the artichokes, sliced side down, in the pan, making sure they lie flat. Cook, shaking the pan occasionally to keep the artichokes from sticking, until they are evenly browned underneath, 6 to 10 minutes. Using tongs, lift to check for doneness.
Place the crushed garlic into the spaces between the artichokes; add the quarters of 1 lemon to the pan, place a piece of foil over the pan and cover with a lid. Reduce heat to medium-low and cook for 8 to 10 minutes more. Remove pan from heat and keep covered. Let artichokes cool to room temperature.
Transfer the artichokes to a serving platter. Squeeze juice from the cooked lemon wedges into the pan and whisk to scrape up any browned bits. Pour juice over the artichokes, garnish with the remaining lemon quarters and serve. 4 servings.