Beat the softened cream cheese, sugar, egg yolk, and vanilla until smooth. Cover and chill in the fridge while you make the batter.
Make the Muffins
Preheat the oven to 425F. Line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the pumpkin puree, granulated sugar, brown sugar, oil, eggs, and vanilla until smooth.
Add the flour, baking soda, baking powder, pumpkin pie spice, and salt. Stir until just combined. Do not overmix.
Spoon a little batter into each liner, about a third of the way up. Add a rounded spoonful of the chilled cream cheese filling to the center, then cover with the remaining batter so the filling is tucked inside.
Bake at 425F for 5 minutes. Without opening the oven, reduce to 350F and bake another 13 to 16 minutes, until the pumpkin springs back and a toothpick in the muffin edge comes out clean. Cool in the pan 10 minutes, then transfer to a rack.
Notes
Chill the filling: A cold, firm dollop holds its shape in the center instead of melting away.
Dollop, don't overfill: A rounded spoonful is plenty. Too much and it leaks out the top.
Storage: Because of the cream cheese, keep these in the fridge up to 5 days, or freeze up to 3 months.