In an electric mixer, cream butter and sugar on medium high until smooth, about 2 minutes.
Beat in egg, vanilla, milk until combined.
Slowly mix in flour, baking powder and salt until just incorporated.
Form the dough into ball and wrap with plastic wrap.
Refrigerate for at least 2 hours.
Preheat oven to 375.
Roll chilled dough to 1/4 inch thickness on a work surface dusted with flour.
Use whatever cookie cutters you have and cut shapes until all dough is used.
Bake for 10-11 minutes.
Let cookies cool on baking sheet for 5 minutes. Remove from baking sheet and cool completely on wire racks before icing.
For the icing, mix powdered sugar, 1/8 cup milk and vanilla. If icing is too thick, continue adding milk, 1 Tbsp at a time. For the icing that you pipe with, you don’t want it too runny.
Scoop icing into a plastic bag. Zip shut and cut a small hole in one corner to use as a piping bag. Pipe your cooled cookies.
Let the icing set for 1 hour.
Add a few more tablespoons of milk to your icing to thin it out. Spoon onto the center of the cookies. Use a toothpick to spread it to the edges. Add sprinkles, sugar or other decorations while the icing is wet so that it adheres. Let cookies cool for another 2 hours.
Store cookies in an airtight container.