Preheat oven to 350°F Spray baking sheet with vegetable cooking spray.
Place flour, sugar, baking powder and salt in food processor bowl. Cover and pulse until blended. Add almond paste and butter. Cover and pulse until mixture forms coarse crumbs. Turn mixture into mixing bowl.
Add almonds, pistachios and chocolate. Beat together whole eggs and egg yolk with a fork. Remove 2 teaspoons and set aside for egg wash.
Make a well in flour mixture. Add remaining eggs and vanilla and stir until mixture holds together. With floured hands, shape dough into four (12-inch-long) logs. Place logs 2 inches apart on prepared baking sheet. Flatten each log to a width of 1 1/4 inches. Lightly brush logs with reserved egg wash.
Bake for 25 to 35 minutes or until logs start to brown and no imprint remains when pressed lightly with finger. Cool on baking sheet on wire rack for 20 minutes.
Reduce oven temperature to 325°F Carefully transfer logs to a cutting surface. Cut logs on the diagonal into 1/2-inch-thick slices. Place biscotti standing up 1/2 inch apart on two ungreased baking sheets.
Bake 15 to 25 minutes more or until biscotti are dry and the sides begin to color slightly. Do not overbake. Cool biscotti on baking sheets for 5 minutes. Transfer to wire racks and cool completely. Store biscotti in an airtight container in a cool, dry place.
*To toast almonds, spread on baking sheet. Bake at 350°F for 8 to 10 minutes or until toasted.