Grease 13 x 9 x 2-inch baking dish. Combine bread cubes and dried and fresh dates in baking dish, making sure that they are evenly distributed.
In bowl, beat eggs and yolks on medium speed until frothy. Add sugar; beat until thick and pale, 3 minutes. On low speed, beat in half-and-half, vanilla and nutmeg until combined.
Spoon custard over bread mixture in baking dish. Refrigerate 30 minutes to 1 hour to let bread absorb custard; push bread down occasionally.
Heat oven to 375 degrees F. Bake pudding 20 minutes. With wooden spoon, push bread down and spoon any liquid custard over top of bread. Bake 15 to 20 minutes longer or until knife inserted in center comes out clean.
Let pudding cool slightly on rack 10 minutes. Dust with confectioners sugar. Spoon onto dessert plates. Serve with crème fraîche on the side. Pudding can be prepared a day ahead. Serve chilled or reheated. Makes 12 servings.