Lightly oil a baking sheet and dust it with flour, tapping out the excess. Preheat oven to 375 degrees F.Advertisement
Place half of the walnuts and hazelnuts in a food processor or blender and pulse until they resemble coarse meal but not powder. Coarsely chop the remaining nuts.
Sift together all-purpose flour, whole-wheat flour, baking soda and salt in a large bowl. Stir in brown sugar and the ground and chopped nuts.
Beat together 1 whole egg and 1 egg yolk in a smaller bowl, reserving the second white. Stir in vanilla and orange zest. Make a well in the center of the dry ingredients, pour in egg mixture and mix thoroughly. The dough will be stiff.
Shape dough into three 18-inch-long, 1/2-inch-thick ropes. Arrange the ropes on the prepared baking sheet and brush them lightly with the reserved egg white. Bake them for 20 minutes. Cut the rolls into diagonal slices about 1/2 inch wide. Reduce the oven heat to 225 degrees , and bake again until the biscotti are crisp and browned, 20 to 30 minutes.
Tip: To toast chopped nuts: Place in a small dry skillet and cook over medium-low heat, stirring constantly, until fragrant and lightly browned, 2 to 4 minutes.