1. Brown the Butter: In a light-colored saucepan, melt the 1 cup of unsalted butter over medium heat. Continue cooking, stirring occasionally, until the butter turns a rich golden brown and nutty-smelling flecks appear at the bottom of the pan. This usually takes 5-7 minutes. Immediately pour the brown butter into a large mixing bowl to stop the cooking process and let it cool for about 5 minutes.

2. Combine Wet Ingredients: To the slightly cooled brown butter, add 1 cup of the granulated sugar, the large egg, vanilla extract, and pumpkin puree. Whisk everything together until the mixture is smooth and well combined. The mixture should be a light orange color and creamy.

3. Mix Dry Ingredients: In a separate medium bowl, whisk together the all-purpose flour, cream of tartar, baking soda, and salt. Make sure there are no lumps and the ingredients are evenly distributed.

4. Combine Wet and Dry: Gradually add the dry ingredients to the wet ingredients, mixing on low speed with an electric mixer or by hand with a spatula until just combined. Be careful not to overmix; overmixing can lead to tough bars. The dough will be thick and slightly sticky.

5. Prepare Cinnamon Sugar Topping: In a small, shallow dish, combine the remaining ½ cup of granulated sugar with the 2 tablespoons of ground cinnamon. Stir well to create your snickerdoodle topping.

6. Assemble and Bake: Press the dough evenly into a greased 9×13 inch baking pan. Sprinkle the cinnamon-sugar mixture generously over the top of the dough, ensuring an even coating.

7. Bake to Golden Perfection: Bake in a preheated oven at 350 F (175 C) for 25-30 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out with moist crumbs, not wet batter. The center should look set.

8. Cool and Serve: Let the bars cool completely in the pan on a wire rack before cutting them into squares. This allows them to set properly and makes for cleaner cuts.