In a large bowl, beat the softened butter and 1/2 cup powdered sugar together until smooth and creamy.
Mix in the vanilla extract until fully combined.
In a separate bowl, whisk together the all-purpose flour and salt.
Gradually add the flour mixture to the butter mixture, mixing until just combined.
Fold in the finely chopped pecans until evenly distributed in the dough.
Cover the dough and refrigerate for at least 30 minutes.
Preheat the oven to 350°F. Line baking sheets with parchment paper.
Roll tablespoons of dough into 1-inch balls and place them 2 inches apart on the prepared baking sheets.
Bake for 12 to 15 minutes or until the bottoms are light golden brown.
Allow the cookies to cool on the baking sheets for about 5 minutes.
While the cookies are still warm, roll them in powdered sugar to coat.
Place the cookies on wire racks to cool completely.
Once cooled, roll the cookies again in powdered sugar.