In a large mixing bowl, whisk together the pumpkin puree, granulated sugar, and brown sugar until well blended. Then add in the large eggs, vegetable oil, and vanilla extract, beating until fully combined.
In a separate bowl, combine the all-purpose flour, pumpkin spice, baking soda, and salt. Stir together with a whisk until evenly incorporated.
Slowly add the dry mixture to the wet ingredients, gently whisking until no lumps remain.
Preheat your oven to 350°F (175°C) and line your muffin tin with paper liners or lightly grease each cup. Fill each muffin cup about ¾ full with the batter.
In a medium bowl, beat the cream cheese using a hand mixer until smooth. Add the granulated sugar, egg yolk, and vanilla extract, and mix until combined.
Spoon about 1 tablespoon of the cream cheese mixture onto the top of each muffin batter-filled cup and swirl gently with a toothpick.
Place the muffin tin into your preheated oven and bake for 18 to 20 minutes. They are done when a toothpick inserted comes out clean or with a few moist crumbs.
Remove the muffins from the oven and let them cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
Notes
For best results, use room temperature ingredients. Do not overmix the batter and gently create swirls with the cream cheese mixture.