Preheat your oven to 375°F (190°C) and place paper baking cups into a muffin pan to get ready for filling them with batter.
In a medium bowl, whisk together the all-purpose flour, pumpkin spice, baking soda, and salt until they are well combined and set aside for later use.
In a large bowl, whisk together the pumpkin puree, granulated sugar, brown sugar, eggs, vegetable oil (or melted butter), and vanilla extract until smooth.
Gradually add the dry flour mixture to the wet ingredients and whisk until just combined, ensuring there are no lumps left in your batter before filling muffin tins three-quarters full.
In another medium bowl, beat the room-temperature cream cheese until smooth and creamy; then add granulated sugar, egg yolk, and vanilla extract beating until fully incorporated.
Top each muffin with about one tablespoon of the cream cheese mixture and use a toothpick to gently swirl it into the batter.