Preheat oven to 350 degrees F. Line two baking pans with parchment paper and set aside.
Using an electric mixer on medium speed, beat the butter and sugar together until light and fluffy, about 2 minutes.
Add the egg, vanilla, baking powder, and salt, and mix until combined and smooth, scraping the sides of the bowl as needed.
Reduce the mixer speed to low and gradually add the flour, only mixing until the dough just comes together. Give it a final mix with a rubber spatula, folding and pressing it together, to ensure all of the flour is mixed in.
Separate the dough in half and work with one piece at a time, roll the dough ¼-inch thick. Cut out shapes as desired and place them on the prepared baking sheets, leaving at least 1 inch of space between cookies.
Bake until the cookies look set and are slightly firm to the touch but still pale, about 10 to 12 minutes.
Cool on the baking sheet for 5 minutes, then remove to a wire rack to cool completely.
Notes
Mixer: A stand mixer is ideal for this recipe; since we are starting with cold butter, the paddle attachment does a good job of beating it into the sugar. If all you have is a hand mixer, I recommend using your fingers to smash the cubes of butter into the sugar before starting the mixer to give everything a headstart.
Baking Sheets: I use my favorite rimmed half-sheet pans. I always, always line with parchment paper, not a silicone baking mat (which I find causes more spread).
Rolling Surface: You can use a clean countertop, butcher block, or your favorite non-stick dough mat. A marble pastry board isn't necessary, but if you have one, it’s great for keeping sugar cookie dough and pie crust cold!
Cookie Cutters: You can use absolutely any, so pick your favorites! I have had this 100-piece set for nearly 20 years and I love them... includes all letters, numbers, and cutters for every season and holiday.
Food Coloring: I swear by gel food coloring! It creates a beautifully saturated color without thinning out the frosting.
Flavors: I adore the pure vanilla flavor, but some people like a little bit of almond - I would recommend starting with ¼ teaspoon of almond extract in addition to the vanilla. You can also use things like cake batter extract, lemon, maple, coconut, etc. You can also add a little bit of cinnamon to the cookie dough if you'd like!
Scaling: You can double (or more!) this recipe without issue.
Buttercream frosting: If you want to do a simple frosting (with or without sprinkles!), then I recommend my favorite vanilla buttercream. It is easily colored and tastes amazing!
Storage: The cookies can be stored in an airtight container at room temperature for up to 5 days.
Make-Ahead: While I love that you can whip up these cookies immediately, you can mix together the dough, divide in half and form into disks, wrap in plastic wrap, and refrigerate for up to 2 days.
Freezing the Dough: You can also freeze the dough (place the wrapped disk in a ziploc freezer bag) for up to 1 month; thaw it in the refrigerator overnight, then bring it to almost room temperature, roll it out, and proceed with the recipe.
Freezing the Cookies: These cookies freeze exceptionally well! You can freeze them plain or decorated; if decorated, let the icing set before freezing. Store in an airtight container or ziplock freezer bag (with parchment paper between the layers if they are decorated). The cookies can be frozen for up to 3 months.