Preheat oven to 375°F and line a muffin tin with paper liners.
In a large bowl, whisk together flour, pumpkin pie spice, baking soda, and salt.
In another bowl, combine pumpkin puree, granulated sugar, brown sugar, eggs, oil, milk, and vanilla. Mix until smooth.
Gradually fold the dry ingredients into the wet ingredients until just combined.
In a small bowl, beat cream cheese, sugar, egg yolk, and vanilla until creamy.
Fill muffin liners 3/4 full with pumpkin batter. Spoon a dollop of cheesecake mixture on top of each muffin and swirl gently with a toothpick.
Bake for 18–20 minutes or until a toothpick inserted into the center comes out clean.
Cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.