In a large bowl, with an electric mixer on medium speed, beat butter, 1/2 cup powdered sugar, and the vanilla until smooth.
In a medium bowl, mix flour and baking powder. Add to butter mixture and beat on low speed to mix, then on medium speed until well blended. Stir in pecans.
Shape dough into 1-inch balls and place about 1 inch apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets.
Bake in a 300° regular or convection oven until cookies are pale golden brown, about 25 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. Let cookies stand on sheets until cool enough to handle.
Place remaining 1 1/2 cups powdered sugar in a shallow bowl. Gently turn warm cookies, a few at a time, in powdered sugar to coat. Set cookies on racks to cool completely.