Stir together first 3 ingredients. Cut butter into flour mixture with a pastry blender or 2 forks until crumbly.
Whisk together yeast and warm milk. Let stand 10 minutes. (Mixture does not foam.) Stir in egg and vanilla. Add milk mixture to flour mixture, stirring until dry ingredients are moistened. Divide dough into fourths; wrap each portion in plastic wrap, and chill 30 minutes.
Roll each portion of dough to 1/8-inch thickness on a flat surface lightly dusted with powdered sugar. Cut dough with a 3 3/4-inch snowflake-shaped cookie cutter. Place on parchment paper-lined baking sheets. Sprinkle with sparkling sugar.
Bake at 350° for 10 minutes or until lightly golden. Cool cookies on baking sheet 5 minutes. Remove to wire racks, and let cool completely.