Cream butter with sugar, soda, salt, and flavorings until fluffy.
Add eggs, one at a time.
Add flour and baking powder and beat until combined.
Chill the dough until firm, but if you leave it in the fridge at least overnight or for a few days, the color and flavor will be better.
Roll out on a floured surface (the thicker you roll, the softer the cookies, and the dough is easier to roll out if it's very cold) and bake at 450 degrees 6-8 minutes. Cool on racks, ice and decorate.
Icing
For the icing I just put a bunch of powdered sugar in a bowl and add heavy cream until it is thin enough to brush on smoothly - really a glaze more than a frosting. I brush it on the cookies and let dry.
Notes
Adapted from from the LA Times Cookbook, originally served at the Valley Hunt Club in San Marino, CA (where I took swimming lessons when I was five)
Recipe by The Domestic Front at http://www.thedomesticfront.com/santa-claus-is-coming-to-town-holiday-sugar-cookies/