Cream the butter and sugar together in the bowl of a stand mixer. Beat in eggs and vanilla. Stir in flour, baking powder and salt. Cover and chill the dough for at least one hour to overnight.
Preheat oven to 400 degrees. Roll out the dough on a floured surface ¼-1/2 inch thick. Cut into shapes with cookie cutters. Place cookies 1 inch apart on a parchment lined baking sheet.
Bake 6-8 minutes. Cool completely before decorating.
Decorating Icing
Mix together the powdered sugar and ¼ cup milk.
Add in the vanilla extract and corn syrup. Mix well.
Make the outline icing the consistency of toothpaste.
Add milk, one tablespoon at a time, to make the icing the consistency of syrup for the fill icing.