Trim the artichokes, and boil for 8 to 10 minutes in salted water till they are just beginning to be tender, but are still quite firm. Drain thoroughly, remove the centre leaves, and with a small sharp knife remove the choke. Stuff the artichoke with fillets of anchovies, mixed with the garlic, pounded together in a mortar. Put a piece of fat bacon over each artichoke, tie with a string and place the artichokes in a saucepan on the chopped vegetables with the oil and a little water. Cover the saucepan and simmer very gently for about 45 minutes, basting occasionally. For serving, remove the bacon from the artichokes, put them on a hot dish and strain a little of the contents of the pan over them.