Preheat your oven to 325°F (163°C) and grease a 9-inch springform pan, lining the bottom with parchment paper.

In a mixing bowl, whisk together all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until well combined.

In another bowl, beat eggs with granulated sugar, light brown sugar, vegetable oil, and vanilla extract until smooth and frothy.

Gradually combine dry and wet ingredients, then fold in shredded carrots and chopped nuts, if using.

Pour the carrot cake batter into the prepared pan and smooth it out.

In a clean bowl, beat cream cheese until smooth, then mix in granulated sugar, all-purpose flour, vanilla extract, and eggs one at a time. Finally, mix in sour cream.

Pour the cheesecake mixture over the carrot cake layer in the springform pan.

Bake for 50-60 minutes, until the center is just set with a slight jiggle.

Cool the cheesecake in the oven with the door cracked for 30 minutes.

Let it cool completely at room temperature for about 1 hour, then cover and chill in the refrigerator for at least 4 hours or overnight.

Carefully remove the cheesecake from the springform pan, top as desired, and serve.