Vanilla Sugar Cookie Sandwiches

1. In a medium bowl, stir together the flour, cream of tartar, baking soda, and salt.
2. In a large bowl, beat the butter on low speed for 30 seconds. Add granulated sugar and beat until smooth and creamy. Beat in milk, and vanilla. Beat in the flour mixture. Dough will be soft.
3. Divide dough in half and wrap each in plastic wrap. Chill dough for 30 minutes. On a lightly floured surface, roll half the dough at a time. Using fluted cookie cutters, cut out the dough: 3″ cutter for the large cookie, and 1″ for the inner cookie. (It will look like a doughnut when you’re done cutting.) Only make half of the cookies in the doughnut shape and for the other half, use only the 3″ cookie cutter. This half will be the bottom of the sandwich.
4. Preheat oven to 350 degrees. Keep re-rolling dough and cutting out circles until all dough is used. Place cookies on a baking stone, and sprinkle cookies with vanilla sugar. Bake cookies for 8-10 minutes.
5. While cookies are cooling, mix cream cheese, powdered sugar and vanilla in a medium-sized bowl, until smooth and creamy.
6. Once cookies have cooled, spread the bottom side of a cookie with the cream cheese mixture and place the doughnut-shaped cookie on top of the cream cheese cookie, making a sandwich.