In a large bowl, whisk together flour, baking powder and salt. Set aside.
Cream the butter and sugar in the bowl of an electric stand mixer fitted with the paddle attachment until light in color, about 1 minute. Add the egg, vanilla extract and heavy cream and beat to combine.
Put mixer on low speed and gradually add the flour mixture, beat until mixture pulls away from the sides of the bowl. First, add only 3 cups of the flour mixture, and if the mixture is still very soft add the rest of the flour. Make sure to scrape the sides of the bowl as needed using a rubber spatula. Divide the dough in half, wrap in plastic wrap, and refrigerate for 2 hours.
Preheat oven to 375 degrees F.
Sprinkle your working surface with a little powdered sugar. Remove one wrapped pack of dough from the refrigerator, sprinkle rolling pin with powdered sugar, and roll out dough to ¼-inch thick. Using a stainless steel square cookie cutter, cut into squares and place at least 1-inch apart on a baking sheet covered with parchment paper.
Bake for 7 to 9 minutes or until cookies are just beginning to turn brown around the edges. Rotate cookie sheet halfway through baking time.
Remove from oven and let cookies sit on the baking sheet for 2-3 minutes before transferring to a cooling rack.
The cookies must cool completely before icing.
Cookies can be stored in an airtight container for up to 1 week.