In a medium bowl, beat together the butter, sugar, egg, milk, and vanilla. Then add the flour (start with 2 cups), baking powder, and salt. Beat this until well blended. If the dough is still really sticky you may mix in another ¼ to ½ cup of flour.
Divide the cookie dough into 2 equal-sized disks. Wrap these and chill them in the refrigerator for 1 hour. When you remove the dough from the fridge, allow it to sit at room temperature until soft enough to roll easily.
Preheat the oven to 375°F.
On a lightly floured surface, roll out the dough to ¼ inch thick.
Use a 2½-inch, lightly floured round cookie cutter to cut out as many cookies as you are able to.
Place the cookies 1-inch apart on ungreased baking sheets.
Bake for 7 to 10 minutes or until the edges are just golden. They can cook quickly so watch carefully after the 5-minute mark.
Transfer the cookies to cooling racks to cool completely before frosting them.