Prep the pan: Heat oven to 350°F (175°C). Line a 12-cup muffin tin with liners or grease lightly.
Make the filling: In a bowl, beat cream cheese, sugar, vanilla, and flour until smooth and fluffy.
Set aside. The mixture should be spoonable but not runny.
Mix dry ingredients: In a large bowl, whisk flour, granulated sugar, brown sugar, baking soda, baking powder, salt, and pumpkin pie spice until combined and lump-free.
Combine wet ingredients: In a separate bowl or large measuring cup, whisk pumpkin puree, eggs, oil, milk, and vanilla until smooth.
Bring it together: Pour wet ingredients into dry. Stir gently with a spatula until just combined.
A few small streaks of flour are okay. Do not overmix.
Fill the cups: Add about 2 tablespoons of batter to each muffin cup (roughly 1/3 full). Use the back of a spoon to nudge batter up the sides slightly.
Add the creamy center: Place a heaping tablespoon of cream cheese filling in the center of each cup. Keep it away from the edges for a neat, creamy pocket.
Top with batter: Cover each with another 1–2 tablespoons of batter, sealing the cream cheese.
Muffin cups should be about 3/4 full.
Optional sparkle: Sprinkle coarse sugar on top for a light crunch.
Bake: Bake 18–22 minutes, until the tops spring back lightly and a toothpick inserted in the muffin portion (not the cream cheese) comes out clean or with a few moist crumbs.
Cool: Let muffins cool in the pan for 5 minutes, then transfer to a rack. Cool at least 20 minutes before eating so the center sets.