Set the oven rack to the upper-middle and lower-middle position. Preheat to 325ºF (160°C).
Line two baking sheets with parchment paper and set aside.
Toast the walnuts in the oven on a small baking sheet for 6 minutes, stirring halfway through. Transfer to a plate and allow to cool for 10 minutes.
Add 1 cup of walnuts to a food processor and pulse about 15 times until finely ground texture is achieved. Transfer to a medium-sized bowl.
Add the remaining 1 cup of walnuts to the food processor and pulse 3 to 5 times, until roughly chopped. Add to the finely ground walnuts.
Add flour and salt to the walnuts, stir to combine.
Using the paddle attachment on a stand mixer or hand mixer, cream the softened butter and granulated sugar on medium speed, 3 minutes. Scrape down sides of bowl halfway through.
Add vanilla and mix on low speed until incorporated, 30 seconds.
Add the walnut mixture and combine on low speed until just incorporated and dough comes together for about 30 seconds.
Measure the dough into leveled 1 tablespoon (15g, ½ ounce) portions. Roll into a ball and place 1-inch apart on the baking sheets, they should be about 1-inch in diameter. Bake 20 to 23 cookies per pan.
Bake until lightly golden in color and the bottoms are browned about 16 to 18 minutes. Rotate the pan and switch positions halfway through baking.
Cool the cookies on the pan for 5 minutes.
Add powdered sugar to a shallow bowl. Roll the cookies inside while still warm until completely coated, then transfer to a wire rack to cool.
Once cooled, roll them in powdered sugar for a second coat or sprinkle on top with more sugar, shaking off any excess. This can be done right before serving for the most attractive appearance.
Roasted walnuts can be used instead of raw. Skip toasting (step 3) if using pre-roasted nuts.
Pecans can be substituted for walnuts.
Make it Gluten-Free: Substitute gluten-free flour for all-purpose flour. I recommend Bob’s Red Mill 1:1 gluten-free baking flour.