Start by preheating your oven to 350°F and lining your baking sheets with parchment paper for easy cleanup.
In a large bowl, cream together the softened butter and granulated sugar with an electric mixer until the mixture is light and fluffy.
Beat in the egg, egg yolk, and vanilla extract until the mixture is smooth and well incorporated.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, and 1/2 teaspoon of table salt.
Gradually mix the dry ingredients into the wet ingredients until a dough forms. Be careful not to overmix.
Prepare the cinnamon swirl by combining the light brown sugar, ground cinnamon, 1/8 teaspoon table salt, and softened butter in a bowl. Mix until it resembles a paste.
Fold the cinnamon paste into the cookie dough, creating swirls. Do not fully mix it in; you want to see the cinnamon swirl in the cookies.
Scoop the dough onto the prepared baking sheets, spacing the cookies about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers should still be soft.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.