Preheat oven to 350ºF, and spray an 8-inch square baking dish with nonstick cooking spray.
In a large bowl, whisk the flour, baking powder, spices, salt, and sugar together until combined. Add the pumpkin puree, sour cream, milk, eggs, and vanilla, mixing until batter is almost combined. Pour in the melted butter and continue mixing until smooth.
Pour half of the batter into the prepared pan. Drop spoonfuls of half of the brown sugar swirl mixture over the batter. Add remaining batter on top, followed by spoonfuls of remaining swirl mixture. Using a skewer or knife, swirl figure-eights throughout the batter.
Bake in the oven for 30-35 minutes, or until the top is set and center of the cake jiggles slightly. Allow to at least 10 minutes before spreading frosting on top.