In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, pumpkin pie spice, and nutmeg. Set aside. Spread the pumpkin puree on a plate and press a paper towel onto it to absorb excess moisture; repeat 3 to 4 times until the puree feels drier.

In a separate bowl, mix the melted butter, pumpkin puree, brown sugar, egg, vanilla, sour cream, and buttermilk until smooth. Pour the wet mixture into the dry ingredients and stir just until combined—do not overmix.

Preheat the oven to 425°F. Line a 12-cup muffin pan with 6 paper liners, spacing them out so the muffins have room to rise tall.

Use a large cookie scoop to drop a heaping scoop of muffin batter into each liner. Sprinkle the tops generously with coarse sugar.

In a small bowl, beat the cream cheese, granulated sugar, flour, milk, and vanilla with a hand mixer on high speed until smooth and creamy.

Transfer the cream cheese filling to a piping bag. Snip off the tip and pipe a dollop into the center of each muffin, using all the filling evenly among the 12 muffins.

Bake at 425°F for 8 minutes, then reduce the oven temperature to 350°F and bake for another 6 to 8 minutes, until a toothpick inserted into the muffin (avoiding the filling) comes out clean.

Let the muffins cool in the pan for 10 minutes, then transfer them to a wire rack to cool completely. Store in the refrigerator—these taste best chilled.