Cut the top quarter off the artichoke with a serrated knife. Snap off and discard any battered outer leaves. Using scissors, trim the remaining barbed leaf-ends of the artichoke. Cut the stem flush with the artichoke body. Rub the cut surfaces with a lemon half.
Fit a medium pot large enough to hold the artichoke with a steamer basket. Slice the remaining lemon and use it to line the steamer. Arrange the herb sprigs and garlic over the lemon. Put the artichoke stem-end up in the center of the steamer. Add enough water to come up to the bottom of the steamer. Cover and steam over medium-high heat, adding more water if necessary, until outer leaves can be easily removed from the artichoke and the base can be readily pierced with a knife, about 40 minutes. Serve the artichoke warm with melted butter or oil, or chilled with mayonnaise or oil.