1) Preheat the oven to 350°F. Lightly grease (or line with parchment) one large (about 18" x 13") baking sheet.
2) In a medium-sized bowl, beat the butter, sugar, salt, flavor, vanilla, and baking powder until the mixture is smooth and creamy.
3) Beat in the eggs; the batter may look slightly curdled.
4) At low speed of your mixer, add the flour, stirring until smooth; the dough will be sticky.
5) Stir in the pistachios and cherries.
6) Divide the dough in half, and plop both halves onto the prepared baking sheet, leaving space between them.
7) Shape each half into a long rectangle about 10 1/2" x 2" wide x 3/4" tall; remember, you need to leave space for expansion between the pieces of dough.
8) Straighten the rectangles, and smooth their tops and sides; a wet spatula or wet bowl scraper works well here.
8) Bake the dough for 25 minutes. Remove it from the oven. Using a spray bottle filled with room-temperature water, lightly but thoroughly spritz the two pieces of dough, making sure to cover the sides as well as the top. Softening the crust just this little bit will make slicing the biscotti without crumbling easier.
9) Reduce the oven temperature to 325°F.
10) Wait 5 minutes, then use a sharp chef's or serrated knife to cut the biscotti crosswise into 1/2" to 3/4" slices. Or cut the biscotti on the diagonal, for fewer, longer 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.
11) If you've used parchment on your baking sheet, remove it; save it for another day. Place the biscotti on the baking sheet, on edge; they can be very close together.
12) Return the biscotti to the oven, and bake them for 35 to 40 minutes, until they feel very dry and are beginning to turn golden. They may 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. You'll want to start checking the biscotti around the 30-minute mark; the ones on the ends of the pan, or any smaller biscotti, may be ready to come out of the oven earlier than the larger/middle-of-the-pan biscotti.
13) Remove the finished biscotti from the oven, and cool them right on the pan.
Yield: 3 dozen biscotti.