Preheat the oven to 375 F. Place the butter and shortening in the bowl of a stand mixer and mix until combined, about 30 seconds. Add both sugars, baking soda, and salt.
Mix until combined, stopping to scrape down the sides of the bowl if necessary. Beat in the eggs and vanilla until well combined.
Add flour into the bowl and mix until all the flour disappears. Do not over mix.
Using a spatula or wooden spoon, mix in the chopped pistachios and chocolate chips.
Drop dough onto baking sheets lined with parchment paper using a small cookie scoop. Space cookies about 2 inches apart.
Bake 8-9 minutes, or until the cookies are light golden brown on the edges and slightly underdone on top. Rotate the pans halfway through.
Be careful not to over bake. Cool the cookies on the baking sheets for a few minutes, then carefully transfer them to wire cooling racks. Store leftovers in an airtight container