Cream the butter and sugar. In a stand mixer fitted with the paddle attachment, beat the butter and powdered sugar on medium speed until smooth and creamy (about 1–2 minutes). Then, add the egg yolk, vanilla extract, and salt, scraping down the sides of the bowl as needed, and mix until well combined.
Add the flour. Set the mixer to the lowest speed. Then, add half of the flour and mix until it's just blended. After that, add the rest of the flour and keep mixing until the dough starts to come together. If the dough is still too crumbly after a minute of mixing, add water a few drops at a time until the dough sticks together when you pinch it.
Prepare and chill the dough. Place the dough on a clean surface and cut it into two equal pieces. Form each piece into a flat disc, wrap it well in plastic wrap, and put it in the fridge for at least 2 hours or up to 1 day. Chilling the dough makes it firmer and helps it keep its shape while baking.
Preheat and soften the dough. Preheat your oven to 350°F (175°C). Then, line baking sheets with parchment paper or silicone baking mats. Next, take one dough disc out of the fridge and let it sit for a bit until it’s easy to roll out. If the dough gets too soft while you're working with it, just put it back in the fridge for a few minutes.
Roll and cut the cookies. Sprinkle some flour on your work area and get your rolling pin. Then, roll the dough out to about ⅛–¼ inch thick, making sure it’s even for consistent baking. Use cookie cutters to make shapes, putting them close together to reduce leftover dough. You can roll the leftover pieces again to keep the dough from getting tough. Next, place the cut cookies on the baking sheets, leaving about an inch of space between each one.
Bake. Bake in the preheated oven for 12–15 minutes, rotating the trays halfway through for even baking. Thinner cookies will bake closer to 12 minutes, while thicker cookies may take up to 15 minutes. The edges should be just slightly browned. Be careful not to overbake.
Cool and decorate. Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. Decorate with your choice of glaze, royal icing, or buttercream, and add sprinkles.