Preheat oven to 350°. Combine first 5 ingredients in a medium bowl, and beat with an electric mixer at medium speed until smooth and creamy. Add eggs, and beat until blended. (Batter may look slightly curdled.) Add flour, beating at low speed until smooth. (Dough will be soft and sticky but should hold its shape when dropped from a spoon.) Stir in pistachios and cherries.
Transfer dough to a lightly greased baking sheet, and shape into a log about 14 inches long, 2 1/2 inches wide, and about 3/4 inch high.
Bake at 350° for 22 minutes. Remove from oven, and reduce temperature to 325°. Let stand 5 minutes; slice into 3/4-inch pieces. (Cut perpendicular to cutting board so biscotti will be even and not thicker on 1 side.)
Stand biscotti on edge on baking sheet. Return to oven, and bake at 325° for 25 minutes. Remove from oven, transfer to wire rack, and cool completely; store in an airtight container.