Preheat your oven to 350°F (175°C) and line two large baking sheets with parchment paper.
In a large mixing bowl, use an electric mixer on medium speed to beat the softened butter and granulated sugar together until the mixture is light and fluffy, about 2-3 minutes. Beat in the vanilla extract until fully incorporated.
Gradually add the flour and salt to the butter mixture, beating on low speed just until the dough begins to come together. Use a spatula to fold in the finely chopped pecans until they are evenly distributed and no dry streaks of flour remain.
Scoop the dough by the level tablespoon and roll it between your palms to form 1-inch balls. Place the dough balls about 2 inches apart on the prepared baking sheets.
Bake for 12-14 minutes, or until the bottoms are just starting to turn a light golden brown while the tops remain pale. The cookies will be soft but will firm up as they cool.
Let the cookies cool on the baking sheet for 5 minutes, then carefully transfer them to a wire rack to cool for another 10 minutes until they are just warm to the touch.
Place the powdered sugar in a shallow bowl. Gently roll each warm cookie in the sugar until it is completely coated, then return it to the wire rack to cool completely. Once cooled, roll each cookie in the powdered sugar a second time for a thick, snowy coating.
