Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper or silicone baking mats.

Cream the Butter and Sugar: In the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter until creamy. Gradually add the 1/2 cup of powdered sugar and beat until the mixture is light and fluffy (about 2 minutes). Beat in the vanilla extract.

Combine Dry Ingredients: In a separate medium bowl, whisk together the flour, 1/2 teaspoon of cinnamon (for the dough), and salt.

Mix the Dough and Nuts: Gradually add the dry ingredient mixture to the wet mixture, beating on low speed until just combined. The dough will be crumbly and stiff. Remove the bowl from the mixer and use a spatula to fold in the finely chopped pecans or walnuts until they are evenly distributed. If the dough is too soft, chill it for 30 minutes before shaping.

Shape and Bake: Roll the dough into uniform balls, approximately 1 inch in diameter. Place them about 2 inches apart on the prepared baking sheets. Bake for 12 to 15 minutes, or until the bottoms are very lightly golden and the cookies are set. They should remain quite pale on top.

Prepare the Coating: While the cookies are baking, combine the 1 cup of powdered sugar and 2 teaspoons of cinnamon for the coating in a shallow bowl. Whisk until the cinnamon is fully incorporated.

First Roll (Warm): Remove the cookies from the oven and let them cool on the sheet for 1 to 2 minutes. They must still be very warm. Gently roll each cookie in the cinnamon sugar coating until fully covered. Place the rolled cookies on a wire rack to cool completely.

Second Roll (Cool): Once the cookies are completely cooled, roll them in the remaining cinnamon sugar mixture one last time. This second coating ensures the classic thick 'snowball' appearance and texture.