1) Preheat the oven to 350°F. Lightly grease two baking sheets, or line them with parchment.
2) In a large mixing bowl, beat together the butter, shortening, and sugar, then add the eggs one at a time, beating well after each addition and scraping down the bowl midway through.
3) Beat in the vanilla, baking powder, and salt. Mix in the flour, 1 cup at a time, until you have a cohesive, well-blended dough.
4) Add the nuts and butterscotch chips, mixing until they're well-distributed throughout the dough.
5) Transfer the dough to a work surface. Divide it into three fairly equal pieces, and shape each piece into a rough 10" log.
6) Transfer the logs to the prepared baking sheets, leaving about 3" between each log; you may or may not need to use both baking sheets. Wet your fingers, and pat the logs into smooth-topped rectangles 10" long x 2 1/2" wide x 7/8" thick.
7) Bake the logs for 20 to 25 minutes, or until they're beginning to brown around the edges. Remove them from the oven, and allow them to cool for 30 minutes. Lower the oven temperature to 300°F.
8) Gently transfer the logs to a cutting surface, and use a serrated knife to cut them on the diagonal into 1/2"-wide slices. Because of the nuts and the nature of the dough, the biscotti at this point are prone to crumbling; just be sure to use a slow, gentle sawing motion, and accept the fact that some bits and pieces will break off. (It's the privilege of the cook to eat these warm, tasty bits and pieces as they're created.)
9) Carefully transfer the slices, cut sides up (and down) to a parchment-lined (makes cleanup easier) or ungreased baking sheet. You can crowd them together, as they won't expand further; about 1/4" breathing space is all that's required.
10) Return the biscotti to the 300°F oven, and bake them for 20 minutes. Remove them from the oven, quickly turn them over, and bake for an additional 20 minutes, or until they're very dry and beginning to brown. Remove them from the oven, cool completely, and store in an airtight container.
Yield: about 60 biscotti.