Preheat your oven to 350°F (175°C) and prepare a bundt pan by greasing it liberally with non-stick spray or butter, then dusting it lightly with flour.

In a medium mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, ground allspice, and salt.

In a large mixing bowl, combine the granulated sugar, brown sugar, and vegetable oil. Beat until well blended and smooth, then add the eggs one at a time.

Mix in the canned pumpkin puree and vanilla extract until just combined.

Gradually add the dry ingredients to the wet mixture and stir gently until just incorporated.

In another bowl, beat the softened cream cheese, additional sugar, egg, and vanilla extract until smooth and creamy.

Pour half of the pumpkin batter into the prepared bundt pan, dollop the cream cheese mixture over, and swirl it through.

Carefully pour the remaining pumpkin batter over the cream cheese layer and dollop the remaining cream cheese on top.

Place the bundt pan in the oven and bake for 50 to 60 minutes, until a toothpick comes out clean.

Remove from the oven and let it cool for 15 minutes before inverting onto a wire rack to cool completely.