Beat butter and sugar with an electric mixer in a large bowl until smooth. Add first egg while continuing to beat, incorporating the egg fully before adding the second and beating fully into the mixture. Beat vanilla extract and almond extract into the mixture with the third egg.
Stir flour, cream of tartar, baking soda, and salt together in a separate bowl; add to the wet mixture and beat just until the wet and dry combine into a cookie dough. Shape dough into a ball, wrap in plastic wrap, and refrigerate until chilled, at least 3 hours.
Preheat oven to 350 degrees F (175 degrees C).
Roll dough out onto a flour-dusted surface and cut with cookie cutters. Arrange cut cookies onto baking sheets.
Bake cookies in preheated oven until beginning to brown around edges, 6 to 8 minutes.
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