Make the cookies: Preheat oven to 350F. Line a baking sheet with parchment paper. Set aside.

Place butter and 1 cup sugar in a stand mixer bowl fitted with a paddle attachment. Beat on medium speed until creamy. Beat in egg and vanilla until smooth.

In a separate medium bowl, whisk flour, cream of tartar, baking soda, 2 teaspoons cinnamon, and salt. Add flour mixture to liquid and beat on medium speed until a dough forms.

Roll dough into 1-in balls and place 1-in apart on prepared baking sheet. Bake cookies at 350F 9-10 minutes (cookies will still seem slightly soft in the middle---this is ok) Cool cookies on a baking sheet 5 minutes then transfer cookies to a cooling rack to cool completely.

Once cookies are cooled, assemble the ice cream sandwiches: Place one medium scoop vanilla ice cream on the bottom of 6 cooled snickerdoodles. Top ice cream with remaining 6 cookies to form a sandwich. Quickly wrap ice cream sandwiches in plastic wrap and place in freezer. Freeze sandwiches at least 30 minutes before serving.