Preheat oven to 350 degrees and oil a baking sheet. Combine flour, salt, baking powder, parmesan, pepper, sage, thyme and walnuts in a bowl.
In a separate bowl, whisk together 3 of the eggs with the cold water. Make a well in the center of the dry ingredients and pour the whisked eggs into the well. Stir until combined.
Flour your hands and a work surface. Knead the dough until smooth, about 4 minutes. Shape dough into a 2 1/2 x 8 inch log. Set on oiled baking sheet. Whisk the remaining egg. Lightly brush over the log to glaze it. Bake until golden brown about 25 minutes. Take out loaf and lower oven to 325 degrees. Let loaf cool to room temp. on a wire rack.
When cooled, use a serrated knife to slice the loaf approx. 1/4 inch thick. Arrange the slices, cut side down, in a single layer on the baking sheet. Return to oven and bake until lightly golden and crisp about 12 minutes. Cool biscotti on a wire rack.