Rinse artichokes and trim tops. Cut base so artichoke will stand up when placed on plate after cooking.
Fill large pot 2/3 full of water. Squeeze lemon halves into water and add to pot. Smash garlic clove with side of knife and add to pot. Add olive oil, vinegar, oregano, salt, and pepper.
Place artichokes in seasoned water and cover pot. Bring to boil over medium high heat, then remove lid.
Boil, turning occasionally, until leaves are easily removed from artichoke, about 45 minutes. Drain well.
Serve with melted butter, mayonnaise, or aioli.