Cut the stems and the tops off each artichoke. Wiggle the artichoke back and forth with your thumbs to open the leaves. Snap off and discard the tough outer leaves.
Place lemon wedges in a large bowl of water. Soak artichokes for 30 minutes.
Remove the artichokes from the water and shake off excess water. Insert slices of pecorino Romano cheese between the artichoke leaves. Place a garlic clove into the centre of each artichoke.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Arrange artichokes upright in the steamer. Drizzle olive oil over the artichokes and water; add salt. Bring water to a boil. Cook artichokes until the cheese in the centre has melted and you can easily pull an outer leaf away, about 1 hour.