Preheat oven to 350. Line a jelly roll pan with parchment paper cut to fit exactly. Blend the flour, walnuts, baking powder and baking soda in a large bowl until the nuts are evenly mixed in. Set it aside nearby. Break 2 of the eggs into a 2-to-3 quart mixing bowl, separate the third egg, then drop the yolk into the bowl but reserve the white in a small bowl. Whisk the eggs, adding the sugar, the zests, and the orange oil. Gradually whisk in the melted butter, and when all is well blended, pour it into the bowl of flour and other dry ingredients. Fold and push all ingredients together until the liquid is absorbed and the dry ingredients have been completely incorporated. Empty it out onto your lightly floured work surface, and knead and squeeze it into a quite stiff, doughy mass.

Divide the dough in half and roll and press each half into a log 14 inches long; press the ends in as you roll to keep them neat. Lift each log as shaped onto the parchment-lined pan, and press the top to flatten slightly-the logs will be oval in shape. Beat the reserved egg white with a fork until smooth and brush it lightly over the tops of the logs.

Bake until the logs are light brown but still give slightly when the tops are pressed, about 30 minutes. Remove the pan from the oven and reduce the temperature to 325. Let the logs scool on the pan for 15 minutes.

One at a time, remove the logs to a board and cut them on a diagonal into 1/2-inch slices. Lay the slices on their sides and return the sheet to the oven. Bake until the cookies are light brown, about 15 minutes. Set them on wire racks, and when the biscotti are thoroughly cold, store them in an airtight container, where they will keep for weeks.