In a mixing bowl, combine the softened cream cheese, granulated sugar, and vanilla extract. Use an electric mixer to beat until smooth and creamy, about 2-3 minutes. This ensures the filling is well-blended and easy to pipe into the muffins.

Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners or grease it lightly.

In a large mixing bowl, whisk together the sifted all-purpose flour, granulated sugar, brown sugar, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt until well combined. This helps to evenly distribute the leavening agents and spices.

In a separate bowl, whisk together the pumpkin puree, eggs, vegetable oil, and milk until smooth. This mixture adds moisture and flavor to the muffins.

Pour the wet ingredients into the dry ingredients and gently fold them together using a spatula until just combined. Be careful not to overmix, as this can lead to dense muffins.

Scoop about 1 tablespoon of muffin batter into each muffin cup, followed by a generous dollop of the cream cheese filling (about 1 tablespoon), and then top with another tablespoon of muffin batter to cover the filling. This layering creates a delicious surprise in the center of each muffin.

Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean. This ensures that the muffins are fully cooked and have a nice rise.

Once baked, remove the muffins from the oven and allow them to cool in the pan for 5 minutes before transferring them to a cooling rack to cool completely. This helps to maintain their moisture.