Place the pistachios in a small bowl and cover with water; set aside for 30 minutes.
Drain the pistachios well and place them on a paper towel to air dry while you assemble the cookie dough.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar and beat on medium-high speed until pale and fluffy. Add in the egg and beat until combined. Add in the flour and pistachios and beat until combined. The dough should be stiff.
Sprinkle 2 tbsp flour over a clean work surface. Scrape the cookie dough onto the surface and gently knead it for 30 seconds. Divide the dough in half, then roll each portion of cookie dough into a log that's roughly 2" in diameter. Wrap each log tightly in plastic wrap and refrigerate for at least 2 hours (or up to 5 days).
When you're ready to bake, preheat the oven to 350°F. Line a large baking sheet with parchment paper.
Remove the dough from the fridge and place it on a cutting board. Using a sharp knife, slice the logs of cookie dough into ¼” rounds. Place the cookies ½“ apart on the prepared baking sheet, and bake for 10 to 12 minutes, or until lightly golden. Remove from the oven and place the pan on a cooling rack. Cool for at least 15 minutes before removing.
