Next, we make the pumpkin coffee cake batter. Preheat the oven to 350°F/175°C and line an 8-inch square or 9-inch round pan (springform works best) with parchment paper. Grease the pan with non-stick spray. NOTE: If you use a 2" tall 8-inch or 9-inch cake pan, make sure to line the sides with a thick strip of parchment paper that is about an inch taller than the sides of the pan, as the cake will bake up taller than the cake pan.
In a large bowl or the bowl of a stand mixer, mix 1 1/2 cups all-purpose flour, 1 cup granulated sugar, 1/3 cup packed light brown sugar, 1 tsp ground cinnamon, 1 tsp pumpkin spice, 1 1/2 tsp baking powder, and 1/2 tsp fine salt until combined.
Add 1/2 cup (1 stick) of room-temperature, unsalted butter that's been cut into 1 Tbsp-sized pieces into the dry ingredients. Mix at low speed with a paddle attachment or hand mixer until the mixture looks like wet sand and no large chunks of butter remain.
Then add 2/3 cup sour cream, 1/2 cup pumpkin puree, 1 large egg, 1 Tbsp of oil, and 1 tsp vanilla extract. Mix on medium speed until fully combined. Scrape the sides and bottom of the bowl as needed with a rubber spatula to make sure everything is properly mixed.
Pour half of the batter (about 450g) into the prepared pan, then sprinkle the cinnamon swirl in an even layer over the batter. Pour the rest of the batter over the cinnamon swirl, and smooth into an even layer that fully covers the cinnamon sugar.