In a large mixing bowl, beat butter and shortening with an electric mixer for 30 seconds.
Add sugar, baking powder, and salt; beat until combined.
Beat in egg, milk, and vanilla until combined.
Beat in as much of the flour as you can with the mixer. Stir in any remaining flour. Divide dough in half. Cover; child dough about 1 hour or until easy to handle.
Preheat over to 375. On a lightly floured surface, roll half of the dough at a time to 1/8 to 1/4-inch thickness. Cut out dough.
Place about 1 inch apart on ungreased cookie sheet. Bake for 7 to 9 minutes or until the edges are firm and bottoms are very lightly browned.
Transfer to wire racks and let cool. Frost with Royal icing and decorate with sprinkles.
ROYAL ICING
2 C. sifted powdered sugar
4 t. meringue powder
1/4 t. cream of tartar
1/4 C. warm water
1 – 2 T. warm water
Stir together powdered sugar, meringue powder, and cream of tartar. Add the 1/4 C. warm water. Beat with electric mixer on low speed until combined.
Beat on high speed for 7 to 10 minutes until very stiff. Add the 1-2 tablespoons additional water, 1 tablespoon at a time, to make desired consistency.