Preheat oven to 375 degrees.
Grease a large cookie sheet; set aside.
In a large bowl beat butter with an electric mixer on medium to high speed for 30 seconds.
Add sugar, cocoa powder, and baking powder; beat until combined.
Beat in eggs, scraping sides of bowl.
Beat in as much of the flour as you can with the mixer.
Stir in remaining flour.
Stir in the 4 ounces chopped white chocolate and the 3 ounces chopped semisweet chocolate.
Divide dough in half.
Shape each half into a 9-inch-long roll.
Place rolls 4 inches apart on prepared cookie sheet; flatten each roll slightly to 2 inches wide.
Bake for 20 to 25 minutes or until wooden toothpick inserted near the centers comes out clean.
Cool on cookie sheet on a wire rack for 1 hour.
Using serrated knife, cut each roll diagonally into 1/2-inch-thick slices.
Lay slices, one cut side down, on an ungreased cookie sheet.
Bake slices in a 325 degree oven for 8 minutes.
Turn slices over and bake for 7 to 9 minutes more or until slices are dry and crisp.
* Do not overbake*
Transfer to a wire rack; cool.
In a heavy, small saucepan combine the shortening and 2 ounces semisweet chocolate.
Cook and stir over low heat until melted and smooth.
Drizzle over tops of biscotti.
Let stand until set.
Store in an airtight container for up to 1 week.