Measure all ingredients and bring butter to room temperature for 30 minutes prior to mixing. Finely chop the pecans to about 1/8 inch pieces.
In a large bowl, cream the softened butter and ½ cup powdered sugar until light and fluffy (approximately 3 minutes). Add vanilla extract and mix until incorporated.
Whisk together flour and salt in a separate bowl. Gradually add this dry mixture to the butter mixture, combining on low speed until just incorporated.
Fold in the chopped pecans using a spatula, distributing them evenly throughout the dough.
Cover the dough and refrigerate for 30 minutes.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Roll tablespoon-sized portions of dough between your palms to form 1-inch balls. Place them 1 inch apart on prepared baking sheets.
Bake for 12-15 minutes until the bottoms are lightly golden but the tops remain pale.
Allow cookies to cool for 5 minutes on the baking sheet. While still warm, gently roll them in powdered sugar, coating completely.
Transfer to a wire rack to cool completely, then roll in powdered sugar a second time for that signature snowball appearance.