Preheat oven to 350 degrees F. In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, brown sugar, baking powder, and salt; beat until combined. Beat in eggs and vanilla. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Stir in the 1/2 cup toffee pieces and chocolate pieces. Divide dough in half (dough will be sticky).
Using floured hands, on a lightly floured surface shape each portion of dough into an 8-inch log. Place logs about 5 inches apart on a greased cookie sheet or a cookie sheet coated with nonstick cooking spray.
Bake about 25 minutes or until golden brown and firm to the touch in the center (logs will spread during baking). Remove from the cookie sheet to a wire rack; cool for 1 hour.
Reduce oven temperature to 325 degrees F. Transfer logs to a cutting board and cut each loaf crosswise diagonally into 1/2-inch-thick slices. (Or, cool completely; wrap and store overnight at room temperature before slicing.) Place slices, cut sides down, on the cookie sheet. Bake for 8 minutes. Turn slices over and bake 8 to 10 minutes more or until dry. Transfer slices to wire racks; cool.
In a small microwave-safe bowl microwave the 6 ounces chocolate and shortening on 70 percent power (medium-high) for 1 minute. Stir. Microwave for 1-1/2 to 3 minutes more, stirring after every 15 seconds until melted. (Or, in a heavy small saucepan heat and stir the chocolate and shortening over low heat until melted and smooth.) Dip one end of each biscotti into melted chocolate mixture. Arrange on a sheet of waxed paper; if desired, sprinkle with additional almond toffee pieces. Let stand until chocolate is set. Makes about 30 biscotti.