Preheat the oven to 350°F. Line an 8x8 inch metal baking pan with parchment paper, leaving enough overhang on the sides to easily lift the cake from the pan once cooled. Lightly spray with nonstick cooking spray.
Add the butter to a light colored saucepan over medium heat. Melt the butter, stirring frequently. It will begin to bubble and foam as it cooks. Continue stirring for about 4-5 minutes, scraping along the bottom of the pan, until the foam begins to subside and small golden brown bits form on the bottom. Once the butter smells rich and nutty and is golden brown, immediately remove it from the heat and pour it, including all of the browned bits, into a large mixing bowl. Allow to cool for about 10 minutes.
Add the brown sugar and granulated sugar to the brown butter and whisk until combined. Add the pumpkin purée, egg, vanilla extract, vegetable oil, and sour cream. Whisk until smooth and completely combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, pumpkin pie spice, and kosher salt. Add the dry ingredients to the wet ingredients and gently fold together with a rubber spatula until just combined. Be careful not to over mix. Spread the batter evenly into the prepared pan.
In a small bowl, stir together the granulated sugar and cinnamon for the topping. Sprinkle the cinnamon sugar generously and evenly over the entire surface of the batter. Do not press it down or swirl it in. Bake for 30–40 minutes, or until the center is set and a toothpick inserted into the middle comes out clean or with a few moist crumbs. Begin checking around 32 minutes to avoid over baking. Allow the cake to cool in the pan before using the parchment paper to lift it out. Slice into squares and enjoy!