In a medium bowl, sift together the flour and baking powder; set aside. In a stand mixer bowl fitted with a paddle attachment, cream the unsalted butter, salt, and sugar until smooth and creamy, about 3 minutes.
Beat in the clear vanilla and pure vanilla extract until well combined. Add the flour mixture and mix until just combined. Place the dough onto a lightly floured work surface and evenly split it into two pieces. Wrap each half in plastic wrap, and refrigerate for at least 1 hour. If chilling for 3+ hours, make sure you let the cookie dough sit at room temperature for at least 10 to 15 minutes before rolling into balls; the cookie dough will be very stiff after being in the fridge that long.
When you're ready to bake, preheat the oven to 350 °F. Remove one of the discs from the fridge and line a cookie sheet with parchment paper. Use a floured rolling pin to roll out the first batch of cookie dough on a lightly floured surface to a rectangle with a thickness of ¼ inch. Next, cut into shapes with any cookie cutter you like. Place cookies 1 inch apart on the prepared baking sheets. Place the cut out sugar cookies in the refrigerator, and take out the second batch of dough. Repeat the rolling and cutting process before transferring them to the second baking sheet. Let the dough chill for 30 minutes.
Preheat the oven to 350 degrees Fahrenheit. Bake the cookies until they are just starting to turn golden at the edges, about 8 to 10 minutes. Let the cookies cool on the baking sheet for about 2 minutes, just until they are firm enough to transfer to a cooling rack with a spatula.
How to Make Icing
In a small bowl, whisk the powdered sugar with evaporated milk (start with 2 tablespoons, you will likely need more milk for the perfect spreading consistency).
Beat in corn syrup and pure vanilla extract until the icing is smooth and glossy; if the icing is too thick, add in a small amount more of corn syrup. Divide into as many bowls as you wish for different colors.
Add in food coloring until desired intensity is achieved. Paint the icing over the cut out sugar cookies using a brush, or dip the edges of cut out sugar cookies into the icing. Sprinkle with colored sugar or other sugar decorations while the icing is still wet. Allow setting on parchment paper or waxed paper. Enjoy our Cut Out Sugar Cookies!