Preheat the oven to 350 degrees F. Spray two muffin tins with cooking oil and set aside.
In a small bowl whisk together flour, baking soda, spices, and salt. In a large bowl combine pumpkin puree with both sugars, mixing to combine. Add apple sauce, oil, and vanilla extract and stir until smooth. Fold dry ingredients into the wet ingredients.
In a separate bowl combine cream cheese, sugar, and vanilla extract with a fork. Stir until smooth.
Fill muffin molds ⅔ of the way full. Top with 1 tablespoon of cream cheese mixture and, using a toothpick, swirl to combine.
Bake for 20 minutes. Remove from oven and allow muffins to cool for 10 minutes before transferring to a wire cooling rack to cool completely.