Preheat oven to 350 degrees F. Line 2 12-cup muffin pans with paper liners; set aside.
In a large bowl, combine flour, sugars, pumpkin pie spice, baking powder, baking soda and salt.
In a large glass measuring cup or another bowl, whisk together pumpkin puree, vegetable oil, eggs and vanilla.
Pour mixture over dry ingredients and stir using a rubber spatula just until moist; let stand for 15 minutes.
Scoop the batter evenly into the muffin tray.
Squeeze about 2 tablespoons cream cheese filling into the center of each muffin, leaving a dollop on the top; sprinkle with rolled oats around the filling, if desired.
Place into oven and bake for 17-22 minutes, or until a tester inserted in the center comes out clean; let cool 10-15 minutes before transferring to a wire rack.
for the cream cheese filling
In a small bowl, whisk together cream cheese, confectioners' sugar, flour, milk, vanilla and salt until smooth. Transfer to a piping bag or Ziploc bag with the corner snipped off.
Notes
Pumpkin puree vs. pumpkin pie filling. Canned pumpkin puree and pumpkin pie filling are not the same, and are not interchangeable. Pumpkin pie filling comes pre-mixed with sweeteners and spices.
Use “brick” cream cheese. Avoid using whipped cream cheese. The “brick-style” cream cheese, at room temperature, will add all the lovely rich and creamy textures for the muffin filling.
Avoid overmixing. Using a rubber spatula, stir the batter until everything is just combined and moistened with a few lumps here and there. Overmixing will lead to dense, tough muffins.
Mix it up. Although not required, feel free to add in chocolate chips, pecans or walnuts to the batter (about 1/2 cup). Or add pumpkin seeds instead of rolled outs, lightly pressing into the batter.
Fill the batter to the top. Fill the muffin cups to the top for bakery-style, domed muffins.
Cool on a wire rack. Cool the muffins on a wire rack for better air circulation, allowing them to cool faster and evenly, and preventing sogginess.
Halve the recipe. Need a smaller-batch of muffins? This recipe halves beautifully yielding 8 muffins with the same bake time.