Heat the oven to 300 degrees. Line two rimmed baking sheets with silicone baking mats or parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, granulated sugar and vanilla on medium speed until light and fluffy. Gradually add the flour, pecans and salt, beating on low speed after each addition until well blended. Using a small ice cream scoop, shape the dough into 1-inch balls. Place half of the dough balls 1 1/2 inches apart on the prepared baking sheets.

Bake until the bottoms of the cookies are lightly browned, about 30 minutes. Transfer to a wire rack to cool slightly.

Place the powdered sugar in a medium bowl and, while the cookies are still warm, roll in the sugar until evenly coated. Transfer to a wire rack set on top of a rimmed baking sheet to cool completely.

Repeat with the remaining dough balls. Serve immediately or store in a tightly-covered container at room temperature for up to 1 week.