Sift together flour, baking powder, and salt. Set aside.
3 cups all-purpose flour, ¾ teaspoon baking powder, ½ teaspoon salt
Place butter and sugar in large bowl of electric stand mixer and beat until light in color.
1 cup unsalted butter, 1 cup granulated sugar
Add egg and heavy cream and beat to combine. Put mixer on low speed, gradually add flour, and beat until mixture pulls away from the side of the bowl.
1 large egg, 1 tablespoon heavy cream
Divide the dough in half, wrap in plastic wrap, and refrigerate for 2 hours.
Preheat oven to 375 degrees F.
Sprinkle surface where you will roll out dough with powdered sugar.
Powdered sugar
Remove 1 wrapped pack of dough from refrigerator at a time, sprinkle rolling pin with powdered sugar, and roll out dough to ¼-inch thick. Move the dough around and check underneath frequently to make sure it is not sticking. (If dough has warmed during rolling, place a cold cookie sheet on top for 10 minutes to chill.)
Cut into the desired shapes, place at least 1-inch apart on parchment/silicone lined baking sheet. Decorate with colored sugars (if desired) and bake for 8 to 10 minutes or until cookies are just beginning to turn brown around the edges. Let sit on baking sheet for about 2 minutes after removal from oven and then move to complete cooling on wire rack.
Icing:
In a medium bowl, mix the confectioners' sugar, vanilla, corn syrup, milk and salt until smooth.
1½ cups confectioners' sugar, ½ teaspoon vanilla extract, 1 teaspoon light corn syrup, 3 tablespoons milk, pinch of salt
It should be quite thick. If it is too thick, add ½ tablespoon more milk. If it is much too thin, add 1 more tablespoon of confectioners' sugar. If you drizzle a little of the icing with the whisk, the ribbon of icing will hold for a few seconds before melting back into the icing. That is when you know it's the right consistency and is ready to use.