Preheat your oven to 375°F and place paper liners into a muffin tin. Set aside.

In a medium-sized bowl, combine the flour, pumpkin pie spice, baking soda, and salt. Mix thoroughly and set aside.

In a large bowl, whisk together the pumpkin puree, granulated sugar, and brown sugar. Add the eggs, vegetable oil, and vanilla extract, and mix well. Gradually add the flour mixture, stirring until the batter is smooth and free of lumps. Fill each muffin cup about three-quarters full.

In a separate bowl, beat the cream cheese until creamy. Mix in the additional granulated sugar, egg yolk, and vanilla extract, and continue beating until the mixture is well blended.

Spoon approximately one tablespoon of the cream cheese mixture onto each muffin. Use a toothpick to swirl it into the batter, creating a marbled effect.

Bake the muffins for 18 to 20 minutes, or until a toothpick inserted into the pumpkin part comes out clean with a few moist crumbs.

Allow the muffins to cool in the pan for 10 minutes before serving warm or cooling completely for storage.