Preheat the oven to 425°F / 220°C. Alternate lining a muffin pan with 6 parchment liners.
Cheesecake Filling
In a small mixing bowl, beat the cream cheese until smooth. Add in the egg yolk, sugar, and vanilla. Beat until thoroughly combined. Set aside.
Pumpkin Muffins
In a small mixing bowl, whisk together the oil, granulated sugar, and brown sugar.
Add in the egg, sour cream, and pumpkin. Whisk until thoroughly combined.
Add in the flour, pumpkin pie spice, baking powder, baking soda, and salt. Gently mix the ingredients together just until no flour streaks remain.
Place ~2 tbsp. of batter in each muffin tin, using a spoon to smooth it out as needed. Top each muffin with 1 tbsp. of cheesecake filling, then smooth it out and distribute the rest of the muffin batter over each muffin evenly. Evenly distribute the remaining cheesecake filling over each muffin, then use a toothpick to swirl it around.
Bake the muffins at 425°F for 5 minutes. Without opening the oven door, reduce the temperature to 350°F / 175°C. Bake for an additional 10-15 minutes, or until a toothpick inserted into the center of the muffins comes out clean.