Small artichokes are delicious! Unlike the mature artichokes, they haven't developed a choke and the whole thing can be eaten, including the stalk.
Just cut away the outer leaves, trim the stalks by an inch or so and peel them. Bring a large pan of lightly salted water to the boil, put in the artichokes, bring back to the boil then cook the artichokes at a simmer for 9 minutes or so.. When they are cooked, cut them in half lengthways, stalk included, and eat them with your favourite sauce - hollandaise, vinaigrette or butter.