Using an electric mixer add butter to a large mixing bowl and beat on high for 30 seconds. Add in the sugar, baking powder and salt and continue to mix until well blended.
Next add in the egg, milk and vanilla and mix until well combined. Occasionally scrape down the sides of the bowl to be sure all the ingredients are fully combined.
Add in the flour a little at a time with the mixer. You may have to mix in the remaining flour with a wooden spoon.
Divide the dough in half and cover each piece with plastic wrap. Chill for at least 1 hour, or longer. (I make the dough a day in advance and keep it in the fridge until I’m ready to bake.)
When dough is properly chilled and you are ready to bake, preheat oven to 375 degrees.
On a lightly floured surface roll out one half of the dough at a time to 1/4-inch thickness. Cut out your shapes using cookie cutters. Place cutout shapes on ungreased cookie sheets 1 inch apart. Using the scraps, re-roll the dough and continue to cut our more shapes. Continue to roll, cut, and repeat.
Bake for 7-10 minutes or until edges are firm and bottoms are very light brown.
Transfer cookies to a wire rack and let cool.
Frost the cookies with sugar icing. Set aside for at least 1 hour or until the icing hardens.