Preheat the Oven - Set the oven rack to both the upper-middle and lower-middle position. Preheat to 325ºF (160°C). Line two baking sheets with parchment paper and set aside.

Roast the Walnuts - Place the walnuts in the oven on a small baking sheet for 6 minutes, stirring halfway through. Transfer to a plate and allow them to cool for 10 minutes.

Crush the Nuts - 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. Combine them with finely ground walnuts. Add flour and salt to the walnuts, and stir to combine.

Mix the Butter and Sugar - 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 the sides of the bowl halfway through.

Add the Crushed Nuts - Add vanilla and mix on low speed until incorporated, 30 seconds. Add the walnut mixture and combine on low speed until just incorporated and the dough comes together, 30 seconds.

Portion the Cookie Dough - Measure the dough into leveled 1 tablespoon (15g, ½ ounce) portions. Roll into balls about 1" in diameter, and place 1" apart on the baking sheets. Place 20 to 23 cookies per pan.

Bake - Bake until lightly golden in color and the bottoms are browned, about 16 to 18 minutes. Rotate the pans and switch positions halfway through. Cool the cookies on the pan for 5 minutes.

Roll in Powdered Sugar - Add powdered sugar to a shallow bowl. Roll the cookies inside while still warm until completely coated, then transfer them 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.