Preheat oven to 350°F (175°C) and line a muffin tin with paper liners.
In a bowl, whisk together flour, sugars, baking powder, baking soda, cinnamon, nutmeg, and salt.
Stir in grated carrots.
In another bowl, whisk together oil, milk, egg, and vanilla.
Combine wet and dry ingredients until just mixed.
In a small bowl, beat cream cheese, sugar, and vanilla until smooth for the filling.
Spoon a tablespoon of batter into each muffin cup, add a teaspoon of cheesecake filling, then top with more batter.
Bake for 18-22 minutes or until a toothpick inserted into the muffin (not the filling) comes out clean.
Cool slightly before serving.