Using the paddle attachment of a stand mixer, or a hand mixer, cream together butter and/or shortening, sugar, and salt, until smooth.
Add eggs one at a time and stir until just fully incorporated. Mix in milk and vanilla extract.
In a separate bowl, sift together flower and baking powder.
Slowly add the flour mixture to the wet ingredients on low speed, mixing until fully incorporated.
Form dough into a ball, wrap in plastic cling wrap, and chill for at least one hour.
When dough has chilled, roll it out on a lightly floured surface until it's about 1/8" thick. Cut out whatever shapes you like and transfer to a cookie sheet lined with parchment paper.
Using a pastry brush, lightly brush the cutouts with milk and sprinkle with granulated sugar before baking.
Bake at 375'F for 8-10 minutes. Remove from oven and let stand two to three minutes before removing from parchment paper to a cooling rack to cool completely before icing.