Trim the artichoke stems to about 3 cm with a stainless-steel knife. Snap off any discoloured leaves with your fingers. Cut off 3 cm from the tops of the artichokes. (For a neater presentation, cut off about 1 cm from the tops of all the remaining outer leaves.) Peel the stems.
Choose a pot large enough to hold a steamer basket with the whole artichokes comfortably. Fill the pot with water to a depth of 3 cm. Add the garlic and rosemary and bring to the boil. Arrange the artichokes in the steamer basket, put the basket into the saucepan, then cover and bring to the boil. Steam for 30 minutes (adding water as necessary) or until a heart is tender when pierced with a knife. Turn the artichokes upside-down to drain. Discard the garlic cloves and the rosemary.
Meanwhile, combine the mayonnaise, sour cream, lemon zest, lemon juice and tarragon in a small bowl. Serve as a dipping sauce with the hot artichokes.