Pre-heat oven to 400 degrees. Line cookie sheets with parchment paper.
Put flour, sugar, baking powder, and salt in a bowl. Cut in softened butter with a pastry blender until the particles are fine. (I actually usually do this in my food processor, but a pastry blender by hand will do just fine.)
After the butter is mixed in, add the egg, milk, and vanilla. Mix thoroughly.
Refrigerate for at least one hour or up to three days.
Roll out the dough on a floured surface until it's 1/8 inch thick. Cut into shapes as desired.
Bake at 400 degrees for 5-8 minutes. Cool completely and frost as desired.