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.over. 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).