1. Brown the Butter: In a light-colored saucepan, melt the 1 cup of unsalted butter over medium heat. Continue to cook, stirring occasionally, until the butter turns a rich amber color and small brown bits form at the bottom of the pan. The butter will smell nutty. Immediately remove from heat and pour into a heatproof bowl to cool slightly. This step is crucial for the unique flavor.

2. Cream Sugars and Butter: In a large mixing bowl, combine the slightly cooled brown butter, 1 cup of granulated sugar, and the 1/2 cup of packed light brown sugar. Beat with an electric mixer on medium speed until light and fluffy, about 2-3 minutes.

3. Add Wet Ingredients: Beat in the large egg until just combined, then stir in the vanilla extract and pumpkin puree. Mix until everything is well incorporated and smooth. The mixture might look a little curdled at this stage, but don’t worry, it will come together.

4. Combine Dry Ingredients: In a separate medium bowl, whisk together the all-purpose flour, baking soda, cream of tartar, 1 teaspoon ground cinnamon, 1/2 teaspoon ground nutmeg, 1/4 teaspoon ground ginger, and salt.

5. Mix Wet and Dry: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix the dough; stop as soon as no dry streaks of flour remain. The dough will be soft and slightly sticky.

6. Prepare for Baking: Preheat your oven to 350 F (175 C). Lightly grease a 9×13 inch baking pan or line it with parchment paper, leaving an overhang on the sides for easy removal. Press the dough evenly into the prepared pan.

7. Add Cinnamon-Sugar Topping: In a small bowl, combine the remaining 2 tablespoons granulated sugar and 1 teaspoon ground cinnamon. Sprinkle this mixture evenly over the top of the dough in the pan.

8. Bake the Bars: Bake for 30-35 minutes, or until the edges are lightly golden and a wooden skewer inserted into the center comes out with moist crumbs attached, but not wet batter. The center should look set. Let the bars cool completely in the pan on a wire rack before slicing and serving.