Combine flour and next 6 ingredients (through salt) in a medium bowl, stirring with a whisk.
Combine vanilla, eggs, and egg white in a large bowl, stirring with a whisk.
Add flour mixture to egg mixture; stir until well blended (it will take time for the dough to come together, but keep stirring!).
Divide dough in half. Turn dough out onto a baking sheet coated with cooking spray.
With floured hands, shape each dough half into a 12" long, by 2" log; pat to ½" thickness.
Bake at 350° for 22 minutes. Remove logs from baking sheet; cool 10 minutes on a wire rack.
Cut each log into 12-14 pieces. Carefully arrange the slices on their sides on the baking sheet.
Bake biscotti an additional 15 minutes or until almost firm (biscotti will be slightly soft in the center but will harden as they cool). Remove biscotti from baking sheet; cool completely on wire rack.