Preheat oven to 350 degrees
Beat butter in large bowl using an electric mixer until light and fluffy. Add 1/2 cup powdered sugar and vanilla; beat until well blended. Beat in flour, then pecans. Divide dough in half; form each half into ball. Wrap separately in plastic; chill until cold, about 30 minutes.
Whisk remaining 1 1/2 cups powdered sugar and cinnamon in pie dish to blend. Set cinnamon sugar aside.
Working with half of chilled dough, roll dough by 2 teaspoonfuls between palms into balls. Arrange balls on heavy large baking sheet, spacing 1/2 inch apart. Bake cookies until golden brown on bottom and just pale golden on top, about 18 minutes. Cool cookies 5 minutes on baking sheet. Gently toss warm cookies in cinnamon sugar to coat completely.
Transfer coated cookies to rack and cool completely. Repeat procedure with remaining half of dough. (Cookies can be prepared 2 days ahead. Store airtight at room temperature; reserve remaining cinnamon sugar.)
Sift remaining cinnamon sugar over cookies and serve.