Preheat oven to 325°. Grease a large baking sheet.
In a small bowl, lightly beat the eggs with the vanilla extract. In a large bowl, combine the flour, baking powder, salt, sugar, and cocoa powder. Blend thoroughly. Add the beaten egg and blend to form a sticky dough. Stir in the chocolate chips.
Cut the dough in half. Flour your hands and shape each half of dough into a 14-inch log. Place the logs on the prepared baking sheet and bake for 30 minutes or until a toothpick inserted in the center comes out clean. Let cool for 10 minutes.
Cut the dough diagonally into slices about ½ inch thick. Place cut-side down on 2 ungreased baking sheets. Bake for a total of 15 minutes, removing the baking sheets from the oven at the halfway point and turning the cookies over. Return to the oven, moving the cookie sheet that was on the top rack to the bottom rack and vice versa (this ensures the cookies cook evenly). Let cool.
Break the white chocolate into pieces. Melt the shortening and chocolate in a metal bowl placed on top of a heavy pot filled halfway with barely simmering water (or use the top of a double boiler if you have one). Melt over low heat, stirring regularly and making sure the chocolate doesn't burn. Use the back of a metal spatula or wooden spoon to spread the melted chocolate over one side of each biscotti. Let dry. Store the biscotti in a cookie tin or other airtight container.
When cutting biscotti dough after the first baking, push down hard on the knife instead of making a sawing motion. “Sawing” the dough can cause it to break into pieces.
Yields about 40 cookies
These taste great served with vanilla ice cream or dipped in a decadent chocolate fondue!