Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter and ¾ cup of sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
In a separate bowl, whisk together the gluten-free flour, baking soda, cream of tartar, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a smooth dough forms.
In a small bowl, mix the remaining 2 tablespoons of sugar with the ground cinnamon.
Scoop out tablespoon-sized portions of the dough and roll them into balls.
Roll each ball in the cinnamon-sugar mixture until well coated.
Place the coated dough balls onto the prepared baking sheet, spacing them about 2 inches apart.
Slightly flatten each dough ball with the bottom of a glass or your hand.
Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
Once the cookies are cooled, place a scoop of ice cream on the bottom of one cookie and top with another cookie to form a sandwich.
Gently press the cookies together to sandwich the ice cream between them.
Repeat with the remaining cookies and ice cream.
Place the assembled ice cream sandwiches on a baking sheet and freeze for at least 1 hour before serving.
Store any leftover sandwiches in an airtight container in the freezer.