In a large bowl, combine butter, eggs and vanilla until well blended. In a separate bowl, combine the flour, sugar, cocoa, baking powder and baking soda; gradually add to butter mixture just until combined. The dough will be crumbly.

Turn dough onto a lightly floured surface; knead in chocolate chips. Divide dough in half. On an ungreased cookie sheet, shape each portion into a 12-inch by 3-inch log, leaving 3 inches between the logs.

Bake at 325 degrees F. for 30 to 35 minutes or until set and tops are cracked. Cool for 15 minutes. Don't cool any longer or you risk the cookies crumbling when you cut them. Carefully transfer to a cutting board; cut diagonally with a serrated knife into 1/2 inch slices.

Place cut side down on ungreased baking sheets. Bake for 20 to 25 minutes or until firm and dry. Remove to wire racks to cool.

For drizzle: Microwave white chips and shortening at 70% power for 1 minute; stir. Microwave at additional 10 to 20 second intervals, stirring until smooth. Drizzle over biscotti.