Sift the flour, baking soda, and salt together.
Cream butter, shortning, and sugars together until very light and fluffy.
Add one egg at a time to the mixture beating well after each addition.
Beat in the milk and vanilla.
Stir in the flour mixture. Cover and chill for 1 hour.
Roll half of the dough to 1/4 inch thickness on a floured surface and cut out cookies. Place them on a parchhment-lined baking sheet 1/2 inch apart and chill 20 minutes.
Preheat the oven to 400 °. Bake cookies for 8 to 10 minutes until cookies just begin to turn golden. Cool on a rack.
When the cookies are completely cool, decorate as desired with Cookie Glaze.