Cover. Bring to a boil and reduce heat to simmer. Cook for 25 to 45 minutes or until the outer leaves can easily be pulled off. Note: artichokes can also be cooked in a pressure cooker (about 15-20 minutes cooking time). Cooking time depends on how large the artichoke is, the larger, the longer it takes to cook. Rinse the artichokes in running cold water. While you rinse them, open up the petals a little so that the water does get inside more easily. 6 In a large pot, put a couple inches of water, a clove of garlic, a slice of lemon, and a bay leaf (this adds wonderful flavor to the artichokes). Insert a steaming basket.