Pulse pecans in a food processor until they are coarse like sand.
Beat butter and 3/4 cup powdered sugar at medium speed with an electric mixer until creamy. Stir in vanilla and ground pecans. Gradually add flour, beating until a soft dough forms. Beat at low speed just until combined. Cover and chill 1 hour.
Divide dough into 5 portions; divide each portion into 12 pieces. Roll dough pieces into 2-inch logs, curving ends to form crescents. Place on ungreased baking sheets.
Bake at 350° for 10 to 12 minutes or until lightly browned. Cool 5 minutes. Roll warm cookies in powdered sugar. Cool completely on wire racks.