Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, cream together the softened butter and 1 ½ cups of granulated sugar until light and fluffy.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix. Cover the bowl with plastic wrap or foil and refrigerate for at least an hour.
In a small bowl, combine the ¼ cup of granulated sugar and ground cinnamon. Mix well and set aside.
Scoop out about 1 ½ tablespoons of cookie dough and flatten it into a disk in your palm.
Place a caramel square into the center of the dough disk.
Fold the edges of the dough around the caramel, completely encasing it, and roll it into a ball.
Roll the dough ball in the cinnamon-sugar mixture until fully coated.
Place the coated dough balls on the prepared baking sheets, spacing them about 2 inches apart.
Bake the cookies in the preheated oven for 10-12 minutes, or until the edges are set and slightly golden but the centers are still soft.
Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Serve the cookies warm for a gooey caramel center, or let them cool completely for a more chewy caramel texture.