Fill a medium bowl with cold water and squeeze in the juice of half a lemon.
Working one at a time, snap off the tough outer leaves of each artichoke until only tender, pale leaves remain. Trim the stems to about 2 inches, peeling off any fibrous outer skin.
Slice off just the very tip of the artichoke. Place the cleaned artichokes immediately into the lemon water to prevent browning.
Flatten the artichokes
Drain and pat the artichokes dry.
On a cutting board, press each artichoke gently, stem up, so the leaves open like a flower. You can also tap them lightly on the board to help spread the leaves.
First fry (to cook through)
In a medium, heavy pot, heat the olive oil to 275°F (135°C).
Add the artichokes stem up and fry gently for about 10–12 minutes, turning once, until tender inside. Use a slotted spoon to remove them to a rack or paper towel. Let cool slightly.
Second fry (to crisp)
Raise the oil heat to 350°F (175°C).
Return the artichokes to the oil, pressing lightly with a slotted spoon so the leaves splay open. Fry for 2–3 minutes, until the leaves are golden brown and crisp.