Cream the butter, cream cheese, and sugar in a large bowl until light and fluffy.
Beat in the egg and vanilla. Add flour and baking powder and stir until combined.
Put dough on a large piece of plastic wrap and flatten it into a disk. Wrap well and chill for at least an hour.
Preheat the oven to 375ºF.
On a floured surface, roll out half of the dough to ⅛-¼ inch thickness. Keep the other half refrigerated until needed.
Using cookie cutters of your choice, cut and place on a parchment-lined cookie sheet at least an inch apart.
Bake for 7 to 9 minutes until cookies start to brown on the edges and are firm.
Cool for a couple of minutes, then remove the cookies to a cooling rack.
To make the frosting, whisk together all ingredients. Start with a tablespoon of milk and add a bit more milk and/or corn syrup to thin it if needed.
