Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Sift flour, cream of tartar, baking soda, and salt together in a large bowl.
Beat butter and white sugar together in a large bowl with an electric mixer until light and fluffy; beat in vanilla extract. Add eggs one at a time, beating well after each addition. Gradually add flour mixture to butter mixture on low speed until dough is just-combined.
Divide dough into 4 portions; refrigerate 3 portions. Roll remaining portion out on a lightly-floured work surface to 1/4-inch thick. Use cookie cutters to cut dough into desired shapes and transfer cookies to prepared baking sheet.
Bake in the preheated oven until slightly golden at the edges, 10 to 12 minutes. Cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. Repeat rolling, cutting, and baking process with remaining dough portions.
