Using the paddle attachment of a stand mixer, cream together butter & sugar for 2-3 minutes on medium speed.
Scrape sides of bowl with a spatula. Add egg & vanilla and mix for 10-15 seconds.
Whisk together dry ingredients in separate bowl. Slowly add dry ingredients into the wet with the mixer on medium speed until incorporated.
Check the consistency of the dough - if it's crumbly at all, use your spatula to scrape the sides of the bowl, especially the bottom, and mix again until the dough is a smooth, even consistency. You don't want to over-mix, but you also don't want crumbly dough.
Wrap the dough in plastic wrap - flattened out a bit so that it chills evenly - and place in the freezer for 30 minutes or in the fridge for at least one hour (or up to a couple of days).
Remove from fridge/freezer. Preheat oven to 375. Break off a chunk of dough at a time, work it with your hands for a little while to soften it up enough to roll out (it does not need to be completely soft - you just want it pliable enough to roll).
Roll dough with floured rolling pin on floured surface to 1/4 inch thickness. Cut shapes & place on baking sheet. (See my notes on baking sheets!) You'll likely be able to fit about 12 regular-sized cutout cookies on one pan.
Bake cookies for 10 minutes. Remove from oven and allow cookies to cool for 5-10 minutes before transferring them to a wire cooling rack.
Repeat process for remaining dough.
Allow cookies to completely cool before decorating. See my notes about decorating below!