Preheat the oven to 350°F Lightly grease (or line with parchment) two large baking sheets.
In a medium-sized bowl, beat the butter, sugar, spices, and vanilla until the mixture is smooth and creamy.
Beat in the eggs; the batter may look slightly curdled.
Gently mix in the flour, crystallized ginger, and diced nuts, stirring until smooth.
Transfer half the dough onto each of the prepared baking sheets, and shape it into a rough, flattened log about 14" long and 1 3/4" wide.
Bake the logs for 20 to 25 minutes. Remove them from the oven, and allow them to cool on the pan for about 30 minutes.
Reduce the oven temperature to 325°F.
Using a spray bottle filled with room-temperature water, lightly but thoroughly spray the logs, making sure to cover the sides as well as the top. Let sit for a few minutes; softening the crust just this little bit will make slicing the biscotti much easier.
Use a serrated knife to cut the logs into 1/2" to 3/4" slices. Cut at a 45° angle for long biscotti; cut crosswise slices for shorter biscotti. As you're slicing, be sure to cut straight up and down, perpendicular to the pan; if you cut unevenly, biscotti may be thicker at the top than the bottom, and they'll topple over during their second bake.
Set the biscotti on edge on the prepared baking sheet. Return the biscotti to the oven, and bake them for 25 to 30 minutes, until they feel very dry. They'll still feel a tiny bit moist in the very center if you break off a piece; but they'll continue to dry out as they cool.
Remove the biscotti from the oven, and transfer them to a rack to cool. Once they're cool, store airtight to preserve their texture. Biscotti can be stored at room temperature for one week; for longer storage, wrap airtight and freeze.