To prepare biscotti, place granulated sugar, molasses, 2 teaspoons vanilla, and 2 eggs in the bowl of a stand mixer.
Beat at high speed until ribbons fall from beaters (about 6 minutes).
Combine flours, spices, and baking powder in a bowl and stir with a whisk.
Add flour mixture to egg mixture, beat at low speed until just combined.
Divide dough in half and place halves on a baking sheet lined with parchment paper.
With lightly floured hands, shape each half into an 8" x 4" loaf.
Lightly beat remaining egg in a bowl and brush tops and sides of the loaves with egg.
Bake at 325° for 35 minutes or until golden brown.
Remove loaves from baking sheet, and cool 10 minutes on a wire rack. Reduce oven temperature to 275°.
Cut each loaf diagonally into 11-15 pieces.
Place slices, cut side down on a clean sheet of parchment on the baking sheet.
Bake at 275° for 8-10 minutes a side, then turning and make an additional 8-10 minutes.
Remove from pan and cool completely on a wire rack.
To prepare icing, combine powdered sugar, milk, and ¼ teaspoon vanilla; stir with a whisk until smooth. Drizzle icing over biscotti; let stand until icing sets.