Preheat the oven to 350°F and grease a 9-inch springform pan.
Mix grated carrots, sugars, oil, and eggs until smooth.
Whisk in flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
In another bowl, beat cream cheese, sugar, eggs, and vanilla until creamy.
Pour half of the carrot cake batter into the pan, then spoon cheesecake batter over it.
Add remaining carrot batter and swirl gently with a knife.
Bake for 60 minutes or until center is just set.
Cool completely and refrigerate at least 4 hours before serving.