Cream together sugar and cold butter with a hand mixer or in a stand mixer with a paddle attachment until combined and fluffy. Add egg and extract and continue to mix until full combined. Slowly add the flour and remove once the dough forms and starts to pull away from the sides of the bowl.
Roll dough between 2 sheets of parchment paper to a thickness of 1/4" or 3/8" thick. Transfer dough to a cookie sheet lined with a silicone mat and top with another cookie sheet. Freeze for 20 minutes.
Preheat oven to 350℉.
Remove dough from freezer and transfer immediately to preheated oven. Bake 8-12 minutes for smaller cookies (less than 2") and 10-16 minutes for larger cookies. Cookies are baked once the bottoms are slightly browned and the tops no longer look wet.
Cool cookies completely before decorating. Store cookies in an airtight container for 5 days. Undecorated cookies will keep in an air tight container in the refrigerator for up to 2 weeks.
Notes
If making a large batch of sugar cookies that you want to all be the same shape/size you can freeze the cut out dough on cookie sheets overnight. Remove the dough from the freezer as you bake it, transferring the dough to a room temperature cookie sheet, then baking.For softer cookies roll them thick (3/8") and leave them to cool on the cookie sheet. For crispier cookies roll them thinner (1/4" or less) and cool them on a cookie cooling rack.