Preheat your oven to 325°F (163°C). Prepare a 9-inch springform pan by lining it with parchment paper and greasing it to prevent sticking.

Combine the dry ingredients for the Carrot Cake Layers by mixing flour, baking soda, cinnamon, and nutmeg in a bowl.

Whisk together the wet ingredients in another bowl: eggs, sugar, vegetable oil, and vanilla extract.

Fold in the grated carrots into the wet mixture, then slowly combine the wet and dry ingredients until just blended.

Pour the cake batter into the prepared pan and bake for 25-30 minutes, then allow to cool completely.

Beat the cream cheese for the Cheesecake Filling until smooth. Add sugar, eggs, sour cream, and vanilla, mixing until creamy.

Spread the cheesecake filling over the cooled carrot cake layer. Bake for another 55-60 minutes, or until set.

Cool the cheesecake gradually by leaving it in the oven with the door ajar for an hour, then refrigerate for at least 4 hours.

Prepare the Frosting by beating together cream cheese, powdered sugar, butter, and vanilla until smooth.

Frost the chilled cheesecake right before serving.