Begin by preheating your oven to 350 degrees F. Spray a 13x9-inch baking pan with baking spray and then line it with parchment paper, allowing some to hang over the sides for easy removal later.

In a large mixing bowl, whisk together the brown sugar, granulated sugar, 6 tablespoons of melted butter, 2 eggs, and sour cream until well combined. Next, add the flour, baking powder, and salt. Continue whisking until the mixture is smooth and lump-free. Pour the batter into the prepared baking pan and spread it evenly using a spatula. Set aside.

In a stand mixer fitted with the paddle attachment, beat the softened cream cheese on medium-low speed until it's smooth and creamy. Add the pumpkin puree and mix until fully incorporated, about two to three minutes. Next, add the remaining 3 eggs and the remaining ½ cup of melted butter, beating until the mixture is smooth. Gradually add the sifted confectioners' sugar, cinnamon, and pumpkin pie spice, continuing to beat until the mixture is well combined and no lumps remain.

Pour the pumpkin mixture over the cake base, spreading it out evenly with an offset spatula. This layer should completely cover the cake base. Bake in the preheated oven for about 40 minutes, or until the center is set but still slightly soft. A toothpick inserted into the center should come out mostly clean with a few moist crumbs.