Preheat the oven to 425°F. Line a 12-cup muffin pan with cupcake liners.
Mix the pumpkin batter. In a large bowl, whisk together the pumpkin purée, brown sugar, and granulated sugar until smooth. Add the eggs, oil, and vanilla, and whisk until combined.
In a separate bowl, stir together the flour, pumpkin pie spice, cinnamon, baking powder, baking soda, and salt. Add the dry ingredients to the pumpkin mixture, pour in the milk, and gently fold until just combined. Don’t overmix—small lumps are totally fine!
Make the cream cheese filling. In a small bowl, beat the cream cheese, sugar, flour, and vanilla until smooth. Add the milk and mix until creamy. Transfer to a small piping bag or a zip-top bag.
Fill the muffin cups. Divide the pumpkin batter evenly among the muffin liners, filling each about ¾ full. Snip a small corner off the piping bag and squeeze about ½ tablespoon of cream cheese filling into the center of each muffin. Add a small swirl on top if you’d like the cream cheese to show.
Bake at 425°F for 5 minutes, then reduce the oven temperature to 350°F and bake another 12–15 minutes, or until a toothpick inserted near the edge comes out clean.
Cool the muffins in the pan for a few minutes, then transfer to a wire rack to finish cooling.