Preheat oven to 350°F (175°C). Line a muffin tin with 12 paper liners.
In a bowl, whisk together granulated sugar, brown sugar, oil, eggs, and vanilla. Stir in grated carrots.
In another bowl, whisk flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Add dry ingredients to wet and mix until just combined.
Divide carrot cake batter among muffin liners (about 1-2 tablespoons each). Set aside.
In a separate bowl, beat cream cheese until smooth. Add sugar and vanilla, then eggs one at a time, beating until smooth.
Spoon cheesecake batter over carrot cake layer in each muffin cup, filling nearly to the top.
Bake 25–28 minutes or until centers are set. Let cool completely, then chill at least 2 hours in the fridge.
Top with whipped cream, chopped walnuts, or carrot decorations before serving if desired.