Beat butter and sugar at medium speed with an electric mixer until fluffy. Beat in eggs and vanilla.
Combine flour and next 3 ingredients in a large mixing bowl.
Add flour mixture to sugar mixture, beating until blended. Stir in pistachios and cherries.
Place half of dough on each prepared baking sheet. Shape each half into a slightly rounded log about 10 x 3 inches using floured hands. (Dough will be very sticky.)
Bake 25 to 30 minutes or until dough is firm to the touch.
Let cool completely on baking sheet on a wire rack.
Transfer logs to a cutting board, and cut into 1/2- to 3/4-inch-wide slices with a serrated knife.
Place slices, cut sides down, on a baking sheet.
Bake 4 minutes on each side or until crisp.
Transfer to wire racks to cool completely.
Dip ends of biscotti in dark chocolate, and drizzle with white chocolate, if desired.