Beat butter at medium speed of an electric mixer until fluffy; gradually add sugar, beating well. Add egg and vanilla, beating well. Combine flour and next 4 ingredients; gradually add to butter mixture, beating until blended. Shape dough into a ball. Cover and chill 30 minutes.
Roll dough to 1/8" thickness on a lightly floured surface. Cut with a 3" angel-shaped cookie cutter, and gently transfer to lightly greased cookie sheets (dough is fragile). Bake at 375° for 6 to 7 minutes or until lightly browned. Carefully remove cookies to wire racks to cool. Place frosting in a microwave-safe bowl. Microwave, uncovered, at HIGH 45 seconds or just until pourable; spoon frosting on top of cookies. Let stand on wire racks until dry.