In a large mixing bowl, cream the softened unsalted butter and 1/2 cup of powdered sugar together on medium speed until light, fluffy, and smooth (about 2 minutes).
Beat in the vanilla extract until fully incorporated.
Turn the mixer to low speed and gradually add the all-purpose flour and salt. Mix just until a crumbly dough begins to form.
Use a rubber spatula to fold in the finely chopped pecans, ensuring they are evenly distributed throughout the dough.
Cover the bowl tightly with plastic wrap and refrigerate for exactly 1 hour to prevent the cookies from spreading in the oven.
Preheat your oven to 375°F (190°C) and line two baking sheets with parchment paper. Pour the remaining 1 1/2 cups of powdered sugar into a wide, shallow bowl.
Scoop the chilled dough and roll it firmly between your hands to form 1-inch balls. Place them 1 inch apart on the prepared baking sheets.
Bake for 10-12 minutes, or until the bottoms are barely golden brown (the tops should remain pale).
Allow the fragile cookies to cool on the hot baking sheets for 5 minutes.
While the cookies are still warm, gently roll them in the shallow bowl of powdered sugar until coated. Place them on a wire rack to cool completely.
Once the cookies are 100% cooled to room temperature, roll them in the powdered sugar a second time for a thick, snowy white coating.