Combine 1 cup flour, soda, and cream of tartar; stir well. Add flour mixture to creamed mixture; beat well.
Combine blueberries and remaining flour; toss until blueberries are well coated. Fold blueberries into batter. Spoon into a well-greased 1 1/2-quart oven proof mold.
Bake, uncovered, at 350° for 1 hour and 10 minutes or until a wooden pick inserted in center comes out clean. Cool in mold 10 minutes; remove from pan, and cool completely. Transfer pudding to a serving dish; slice and serve warm with Hard Sauce.