Prepare the artichokes: Working with 1 artichoke at a time, snap off tough outer leaves until pale-green leaves are exposed. Cut off top third. Using a paring knife, peel dark-green layer from base and stem; trim stem.
Pour oil and 1/2 cup water into a medium deep, heavy pot or Dutch oven. Add artichokes and 1/2 teaspoon salt. Cook over medium-high heat, turning artichokes occasionally, until water has evaporated and oil begins to spatter, about 8 minutes.
Add garlic. Reduce heat to medium; cover pot with a spatter screen or an inverted sieve. Continue cooking artichokes, turning occasionally, until tender and golden brown all over, about 10 minutes. Turn artichokes cut sides down, and press with tongs, wiggling them to separate leaves. Cook until crisp and dark golden brown, 5 to 7 minutes more. Using tongs, transfer artichokes and garlic to paper towels; set artichokes cut sides down to drain. Sprinkle with salt. Serve with lemon for squeezing.