Beat butter and white sugar together in the bowl of a stand mixer using the paddle attachment until light and fluffy, about 3 minutes. Add egg and vanilla extract; beat 1 minute more. Slowly add flour mixture and blend until dough begins to pull away from the sides of the bowl.
Turn dough onto a piece of parchment paper. Knead dough a few times using your hands and form into 2 discs. Wrap each dough disc in plastic wrap and refrigerate for 2 hours.
Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with a silicone mat.
Remove 1 disc of dough from the refrigerator. Place dough on a lightly floured work surface; top with a piece of parchment paper. Roll out dough to about 1/3-inch thickness. Cut dough with round cookie cutters and transfer to the prepared baking sheet.
Place baking sheet with cookies on it in the freezer or refrigerator for 3 to 5 minutes.
Bake in the preheated oven until cookies are just barely beginning to turn golden brown, 8 to 10 minutes. Cool cookies on the baking sheet for 1 minute; transfer to a wire rack to cool completely. Repeat with second disc of dough.
Wipe down all equipment for making the icing with vinegar, including spatulas, measuring cups, and bowls.
Combine confectioners' sugar and meringue powder in the bowl of a stand mixer using the paddle attachment.
Mix water, corn syrup, and clear vanilla extract together in a separate bowl. Pour water mixture into sugar mixture and beat on medium speed until stiff peaks form in the icing, 4 to 5 minutes.
Lemon juice can be used instead of vinegar to wipe down equipment. Wiping down the equipment can help remove trace amounts of grease that will prevent your icing from whipping properly.
Place wooden spoons on either side of your dough while rolling out to guide your rolling pin. They will help you roll out the dough to a nice even thickness.
Placing parchment paper on top of dough while you roll it out allows you to roll out dough without adding additional flour. Adding too much flour can make the dough tough, and can create little pockets of flour in the dough that cause bumps to form on your cookies during baking, making it more difficult to decorate later.
Make the best use of the dough you've rolled out. Every time you re-roll the dough you add a bit more flour, and can create the flour pockets mentioned above.
Only put cookies of similar size on each baking sheet. If you try to bake smaller cookies with larger ones the small ones will be over done before the large ones are baked.
Chilling the cookies prior to baking will ensure they keep their shape while baking.
Per Serving: 244 calories;8.1 g fat;
41.1 g carbohydrates;
2.3 g protein;
28 mg cholesterol;
31 mg sodium.