Position a rack in the center of the oven and heat the oven to 325°F. Line a large cookie sheet with parchment or a nonstick baking liner.
In the bowl of an electric stand mixer fitted with the paddle attachment, mix the flour, sugar, baking powder, and salt on low speed until well blended. On low speed (or with a wooden spoon if mixing by hand), briefly mix in the nuts and cranberries.
In a small bowl or a 1-cup glass measure, whisk together the egg, egg white, orange zest, orange juice, and vanilla. With the mixer on low speed, slowly pour in the egg mixture (mix in with the spoon if mixing by hand). Continue mixing (or mixing with a wooden spoon or your hands), until the dough is well blended and forms a sticky, moist dough, 1 to 2 minutes.
Dump the dough onto the lined cookie sheet. Using slightly damp hands, shape the dough into a 7x11-1/2-inch rectangle, wetting your hands as needed. Press and shape the dough as evenly as possible.
Bake until the rectangle is golden brown on top and slightly darker brown around the edges, about 25 minutes. Transfer the cookie sheet to a rack to cool for about 10 minutes or until it can be easily handled.
Transfer the biscotti to a cutting board; use a spatula to loosen it from the parchment if necessary. Using a serrated knife, cut the biscotti crosswise into slices about 1/3 inch thick. (I use a gentle sawing motion to break through the crust. After that, a firm push down on the knife is all that’s needed.) Discard the parchment, return the slices to the cookie sheet, and arrange them with a cut side down. (It’s all right if they touch because they don’t spread.)
Bake until the biscotti are light golden brown and feel dry, about 14 minutes. Transfer the cookie sheet to a rack and cool the biscotti completely; they’ll crisp as they cool.
The cooled biscotti can be frozen for up to 6 weeks or stored at room temperature for up to 3 weeks, layered between sheets of parchment or waxed paper in an airtight container.