Preheat the oven to 375 degrees F and place baking cups into muffin pan.
In a medium bowl, whisk the flour, pumpkin pie spice, baking soda, and salt until well combined and set aside.
Using a mixer, mix the pumpkin puree, sugar, and brown sugar together.
Then beat in the eggs, vegetable oil, and vanilla extract.
Slowly mix in the flour mixture, adding a little at a time, until combined and there are no lumps in it. Fill muffin cups 3/4 full.
In a medium bowl, beat the cream cheese until smooth. Add in the sugar, egg yolk, and vanilla extract, and beat until completely mixed.
Top each muffin with about one tablespoon of the cream cheese mixture, and use a toothpick to swirl it into the batter.
Bake muffins for about 18-20 minutes, or until a toothpick inserted in the center comes out clean.
Allow to cool and store leftovers in the refrigerator in an airtight storage container. They can be served at room temperature or chilled.