Sift together flour, baking powder, and salt. Set aside. Place butter and sugar in large bowl of electric stand mixer and beat until light in color. Add egg and milk and beat to combine. Put mixer on low speed, gradually add flour, and beat until mixture pulls away from the side of the bowl. Divide the dough in half, wrap in waxed paper, and refrigerate for 2 hours.
Preheat oven to 375 degrees F.
Sprinkle surface where you will roll out dough with powdered sugar. Remove 1 wrapped pack of dough from refrigerator at a time, sprinkle rolling pin with powdered sugar, and roll out dough to 1/4-inch thick. Move the dough around and check underneath frequently to make sure it is not sticking. If dough has warmed during rolling, place cold cookie sheet on top for 10 minutes to chill.
Cut half into rounds with a 4 in round cutter and then cut the second half into rounds and cut your desired shape out of the center of this round. You can use the cut out round and/or you can use the shape. Then place at least 1-inch apart on greased baking sheet, parchment, or silicone baking mat, and bake for 7 to 9 minutes or until cookies are just beginning to turn brown around the edges, rotating cookie sheet halfway through baking time. Let sit on baking sheet for 2 minutes after removal from oven and then move to complete cooling on wire rack
After the cookies have cooled all the way. Spread a thin layer on the bottom round and then top with the round with the cut out and/or with the shape. Dust with powdered sugar and serve.