In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and powdered sugar until combined. Add the egg, vanilla extract and almond extract and mix until well combined.
In a medium bowl, whisk together the flour, baking soda and cream of tartar. Slowly add the flour mixture to the mixer and mix until combined, scraping down the sides of the bowl as needed.
Divide the dough in half and form each half into a disk. Wrap each disk tightly with plastic wrap; cover and chill at least 2 hours, or up to 24 hours.
When you are ready to bake the cookies, preheat your oven to 375 degrees F. Line baking sheets with parchment paper or silicone mats.
On a lightly floured work surface, roll the dough ¼-inch thick. Cut into desired shapes and place on prepared baking sheets, spacing a few inches apart. Chill the cookies in the refrigerator for 15-30 minutes before baking, to reduce spreading.
Bake in the preheated oven for 6-8 minutes, until cookies are barely golden on the bottom. Let cool completely before frosting.