Preheat the oven to 325°F (163°C). Line two baking sheets with parchment paper and set aside.
Place 2 cups shelled pistachios or almonds in a food processor and pulse until finely ground into a crumb; avoid overprocessing into nut butter.
In the bowl of a stand mixer, combine the 3 cups all-purpose flour, 2 cups ground nuts, 1 cup powdered sugar, vanilla, and salt; mix on low to combine.
Add the softened unsalted butter and beat until the dough is smooth and evenly combined.
Use a 1.5 tablespoon cookie scoop or a spoon to portion the dough into balls. Roll each portion between your palms to form smooth balls and place them about 2 inches apart on the prepared baking sheets.
Bake for 15–18 minutes, until the cookies are lightly golden at the edges.
While baking, place the remaining 1 cup powdered sugar in a shallow bowl.
Let the cookies rest on the baking sheet for 2–3 minutes until warm but cool enough to handle, then roll each cookie in the powdered sugar to coat. Return to the baking sheet.
Cool completely on a wire rack before storing in an airtight container.