Preheat oven to 350°F (175°C). Line a 9×13-inch pan with parchment paper, leaving an overhang for easy removal.
In a bowl, whisk together flour, cream of tartar, baking soda, and salt. Set aside.
Beat softened butter until creamy, then mix in 1½ cups sugar until light and fluffy (2-3 minutes).
Add eggs one at a time, mixing well. Stir in vanilla.
Gradually mix in the dry ingredients until a thick, slightly sticky dough forms.
In a small bowl, combine ⅓ cup sugar and 1 tablespoon cinnamon for the swirl.
Spread half the dough into the pan. Sprinkle with the cinnamon-sugar mixture, leaving a small border.
Drop spoonfuls of the remaining dough over the top and gently spread it out.
Mix 2 tablespoons sugar with 1 teaspoon cinnamon and sprinkle over the top.
Bake for 25-30 minutes until the edges are golden and a toothpick inserted in the center comes out with a few moist crumbs.
Cool completely for at least an hour. Lift out using the parchment and cut into squares. Enjoy!