Heat oven to 375º. In a medium bowl, whisk together flour, baking powder and salt. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, sugar and lemon zest on low to medium speed until well blended. Add eggs, one at a time, beating well after each addition. Add vanilla. Gradually add the flour mixture and beat on low speed until just combined. Stir in pistachios.

On a lightly floured work surface, divide the dough in half. (If you have a scale, I think my halves were around 13 ounces each.) Lightly flour each piece and, using your hands, shape it into a log about 9 inches long, ¾-inch thick and 3 inches wide. Transfer to a Silpat or parchment lined baking sheet, placing the logs at least 3 inches apart.

Bake until puffed and lightly browned on top, about 20 minutes. Allow to cool 10 minutes on pan, then transfer to work surface. Using a long, sharp knife, cut each log crosswise into ¾-inch thick slices. Make each cut with a single cut of the blade, as a sawing motion will break the biscotti.

Place the cookies, cut side down, back on the baking sheet. Bake 10 minutes. Remove from the oven, turn each cookie over and bake an additional 10 minutes or until biscotti are golden. Transfer to wire racks to cool.

While the biscotti cool, make the icing. Whisk together powdered sugar, lemon zest and juice in a medium bowl. Adjust as needed by adding more powdered sugar or more lemon juice. Dip one end of each biscotti in the icing, turning to coat the tip evenly. Place back on the wire rack until icing sets.