In the bowl of a mixer fitted with the paddle attachment, using a hand mixer, or mixing with a wooden spoon, cream together butter and sugar.
Mix in eggs and vanilla extract until well combined.
In a separate bowl, whisk together the remainder of cookie ingredients. Add the dry ingredients to the wet in 2 batches, until combined.
Divide dough into quarters, form into discs, and wrap in plastic wrap and chill for at least 20 minutes in the freezer, or 2 hours in the fridge. Meanwhile, preheat oven to 400°F.
After chill time, remove one disc from the freezer or fridge and roll out on a floured surface until the dough is ⅛"-¼" thick.
Cut with cookie cutters and bake on a parchment-lined cookie sheet for 6-8 minutes, watching closely. Cookies are done when bottoms are just barely golden. Remove immediately from cookie sheet, then let cool completely on wire racks before frosting. (Make sure cookie sheets are cool to touch before placing more cookie dough on them.)
Decorate with simple sugar cookie icing (keep it as white icing or add a few drops of food coloring to dye it) and sprinkles, as desired. If you'd like to use sprinkles, apply them before the icing dries.
Notes
Don't stress if the wet ingredients look curdled while mixing! I promise the final dough will turn out perfect.
For rolling out the cookies: you can just a little more flour, or you can use powdered sugar. The powdered sugar absorbs into the cookie while it bakes and doesn't leave any flour residue.
Do not overbake. These cookies could be done in as little as five minutes! You're looking for very slight color along the edges. Err on the side of underbaked.
The cookies will keep on cooking if you leave them on the hot metal pan. Use a large thin spatula to move them to cooling racks as soon as they are out of the oven.
Cool completely before decorating.
This recipe makes a lot! If you want less, you can easily half the recipe. Or do as I do, and freeze the extra dough discs for other holidays.