Cut the stems from the artichoke to form a flat base, and remove any small leaves from the stem end. (These tend to be tough and not very meaty.)
Put a steamer basket* in the bottom of a large stockpot filled with 2-3 inches of water. The water should come to the bottom of the steamer basket. Add the bay leaves, peppercorns, and vinegar to the water, and then place the artichokes on the steamer basket. (I don’t bother to measure the vinegar anymore but just give it a good glug; precise measurements don’t matter here.)
Cover the pot, bring to a boil, then reduce the heat to low and simmer full-size artichokes for 45-50 minutes. Baby artichokes will probably take between 25-35 minutes, depending on precise size. (You should be able to easily pierce through the center with the point of a knife. I thought this seemed like a very long cooking time when I first started cooking artichokes, and I do typically like my veggies al dente. However, the longer cooking time allows you to get more “meat” off the leaves and makes for a tender, delicious heart. That said, the artichokes should not feel mushy or fall apart when lifted from the pot.)
When finished, use tongs to remove to a plate and serve with melted butter, a dollop of mayo, or sauce of choice.