In a stand mixer, cream together the butter and shortening. Add sugar and mix until light and fluffy, 2 to 3 minutes. Add eggs, incorporating one at a time. Add vanilla and milk and mix until combined.
Slowly add flour, baking powder and salt to cookie dough until it is all incorporated. Divide dough in half, form into disks and wrap in plastic wrap. Chill for at least 1 hour or up to overnight.
When ready to bake, preheat oven to 350 degrees F. Line cookie sheets with parchment paper or coat with nonstick spray. Generously flour a flat surface and rolling pin. Divide each disk in half and roll out one portion to 1/4-inch thickness (keep dough not being rolled refrigerated). Cut cookies using 3-inch round cookie cutter. Place on prepared pan 2 inches apart. Bake for 8 minutes. Allow to rest on pan for 2 minutes then remove to a wire rack to cool.
For the frosting: cream the butter until smooth. Add remaining ingredients and cream until light and fluffy, 3 to 4 minutes. Divide frosting into small bowls and color them as you wish with gel food coloring.
Frost cooled cookies and decorate as desired. Store in an airtight container with parchment or wax paper between each layer to prevent them from sticking together.