In a large mixing bowl, whisk the flour, cream of tartar, baking soda, and salt together; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter until smooth, about 1 to 2 minutes. Add the sugar and continue beating on medium speed until smooth and creamy. Scrape down the sides of the bowl, add the egg, and beat just until combined. Add the milk, vanilla, and almond extract and beat on medium-high speed until fully incorporated.
Dump in the flour mixture and beat on low just until combined, about 1 minute. Shape dough into a flat disc, and wrap tightly with plastic wrap. Refrigerate for 2 hours, or until it's less sticky, and easier to handle.