Preheat oven to 350°F (175°C). Grease a 9x13 inch baking pan.
In a large mixing bowl, combine pumpkin puree, sugar, oil, eggs, and vanilla extract. Mix well.
In another bowl, whisk together flour, baking powder, cinnamon, and salt. Gradually add to pumpkin mixture and mix until combined.
Pour batter into prepared baking pan.
In a separate bowl, beat cream cheese, sugar, and vanilla extract until smooth. Drop by spoonfuls over pumpkin batter and swirl with a knife.
Bake for 45 minutes or until a toothpick inserted into the center comes out clean. Cool before cutting into bars.