Sift together the flour, baking soda and baking powder in a medium bowl. Stir in the pepper and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on high speed until pale and light. Add the sugar and beat until light and fluffy, about 7 minutes. Reduce the speed to low and add the eggs one at a time, beating well after each addition. Add the orange zest and vanilla and almond extracts.
Fold in the flour mixture, then fold in the walnuts. Cover the dough with plastic wrap and refrigerate for 30 minutes.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper or nonstick silicone liners.
Divide the dough in half, place 1 piece on each sheet and shape each piece into a 12-inch log, about 2 inches across and 1 inch tall. Bake until the logs are baked through and lightly browned, about 35 minutes.
Let the logs cool for about 10 minutes on the baking sheets (leave the oven on), then transfer them carefully to racks to cool 10 minutes more. Using a serrated knife, slice each log on the diagonal into 3/4-inch-thick slices. Arrange the slices cut-side down on the baking sheets and return to the oven until well toasted, 15 to 20 minutes more. Transfer the biscotti to cooling racks to cool completely. They will keep, tightly covered, up to 1 week.
To toast the walnuts on the stove top, put them in a dry skillet over medium heat and cook, stirring, until golden and fragrant. To toast them in the oven, spread in a single layer on a baking sheet and roast at 350 degrees F until golden and fragrant.
Adapted from "One Dish at a Time: Delicious Recipes from My Italian-American Childhood and Beyond" by Valerie Bertinelli © Rodale 2012. Provided courtesy of Valerie Bertinelli. All rights reserved.