Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners or grease with cooking spray.
In a large mixing bowl, combine the pumpkin puree, vegetable oil, granulated sugar, brown sugar, and eggs. Whisk until smooth and well combined.
In another bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix.
In a separate bowl, prepare the cream cheese filling. Using an electric mixer, beat the softened cream cheese, sugar, egg, and vanilla extract until smooth and creamy.
Fill each muffin cup about halfway with the pumpkin batter. Add a tablespoon of the cream cheese filling on top of the batter, then cover with additional pumpkin batter until each cup is about ¾ full.
Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted comes out clean.
Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
For added flavor, consider including chopped nuts or chocolate chips in the pumpkin batter before baking.