Whisk the flour, baking soda and salt in a medium bowl. Mix the vanilla and egg with a fork in a small bowl.
Beat the butter, granulated sugar and confectioners' sugar together in the bowl of a stand mixer on low speed until the butter has picked up the sugars, about 30 seconds. (If using a hand mixer, beat about 2 minutes.) Increase the speed to medium and beat until slightly creamy, stopping halfway to scrape the bowl, about 1 minute (about 3 minutes with a hand mixer).
Reduce the speed to low, slowly add in the egg mixture and beat until combined. Add the flour mixture a heaping cup at a time in 2 additions, stopping a few times to scrape the bowl and beaters. (If using a hand mixer, increase the speed as the dough gets thicker to keep the beaters spinning.) Once all the flour is just incorporated, add the confetti stars, increase the speed to medium (higher with a hand mixer) and beat until the dough is very smooth, about 2 minutes (about 5 minutes with a hand mixer).
Turn the dough out of the bowl and bring it together. Divide the dough into 2 even pieces, each about 11 ounces. Shape each piece into a 6-inch square and wrap in plastic wrap. Refrigerate the dough for at least 3 hours and up to overnight.
Position oven racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment. Take the dough pieces out of the refrigerator and let soften until just pliable but still cool and firm, about 15 minutes.
Dust a piece of parchment with flour. Dust one square of the dough with flour and roll it to about 1/4 inch thick. Lift the dough occasionally by sliding a metal spatula or bench scraper underneath to make sure it isn't sticking to the parchment. Cut out cookies into stars and letters with 3-inch cutters, as close together as possible; transfer to one of the prepared baking sheets, leaving 1 inch between them. Gather together the scraps and repeat with the remaining dough. Sprinkle more stars over the top of the cookies and gently press down so they stick. Freeze the cookies on the baking sheet while you repeat with the other dough. Freeze the cookies about 10 minutes before baking.
Bake, rotating the baking sheets from front to back and top to bottom halfway through, until the cookies are light golden brown, 18 to 20 minutes. Let cool completely on the baking sheets on a cooling rack, about 30 minutes.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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