In a large bowl, with a mixer on medium speed, beat 1 cup butter, 1/2 cup powdered sugar, and vanilla until smooth.
In a medium bowl, mix flour and baking powder. Add to butter mixture, stir to mix, then beat until well blended. Stir in pecans.
Shape dough into 1-inch balls and place about 1 inch apart on buttered
12- by 15-inch baking sheets.
Bake in a 300º regular or convection oven until cookies are pale golden brown, about 25 minutes. If baking two sheets at once in one oven, switch their 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. Roll warm cookies in powdered sugar to coat all over; discard remaining sugar. Set cookies on racks to cool completely.