In a stand mixer with a paddle attachment (or a hand mixer), cream together the butter, shortening, sugar, and zest until light and fluffy. Add vanilla and orange juice and mix until just combined, scraping down the sides of the bowl as necessary. Add flour, cornstarch, baking powder, and salt and mix until just combined. Add chopped pistachios and mix until evenly distributed.
Divide the dough in two and form each half into logs, about 9-10" long and 1" in diameter. Wrap in plastic wrap, and roll lightly to make the logs smooth and round. Place both logs in the fridge for at least two hours or up to overnight.
Preheat oven to 350 F and line a baking sheet with parchment paper. Remove one cookie dough log from the fridge and cut evenly into slices, just shy of 1/2" thick. Arrange cookies evenly on the baking sheet. One log of cookies should fit onto the sheet. Bake for 12-15 minutes or until the edges of the cookies are very lightly browned. Remove from the oven, allow to cool for a few moments on the sheet, then remove and place on a cooling rack. Repeat process with the other cookie dough log.
Add chocolate chips and shortening to a microwave safe bowl. To assist in the cookie dipping process, try to find one that is narrow and deep. A 2-cup liquid measuring cup works great for this.
Microwave the chocolate and shortening in 30 second increments, stirring after each increment, until chocolate is completely melted and smooth (It should take less than two minutes--be careful not to get the chocolate too hot.)
Dip each cookie halfway into the chocolate and lay on a wax or parchment paper-lined sheet. As the amount of chocolate in the bowl decreases, you can use a spoon to cover the cookie in chocolate. Enjoy!