Preheat your oven to 325°F (163°C) and grease a 9-inch springform pan. In a large mixing bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt until well combined. In another bowl, mix the brown sugar, granulated sugar, vegetable oil, eggs, and vanilla extract until smooth. Gently fold in the grated carrots and chopped nuts, then incorporate the dry ingredients until just combined, taking care not to overmix.

In a separate bowl, beat the cream cheese until smooth and creamy. Gradually add the granulated sugar, continuing to mix until well combined. Add the eggs one at a time, mixing gently after each addition. Finally, stir in the vanilla extract and sour cream until the cheesecake batter is smooth and creamy, ensuring there are no lumps that could affect the texture of the Carrot Cake Cheesecake.

Layer half of the carrot cake batter into the prepared springform pan, smoothing it out evenly. Carefully spoon half of the cheesecake batter on top, spreading it to cover the cake layer. Repeat by adding the remaining carrot cake batter followed by the rest of the cheesecake batter. Use a knife to gently swirl through the layers, creating a marbled effect that adds visual appeal to the Carrot Cake Cheesecake.

Place the assembled cake in the preheated oven and bake for 50-60 minutes, or until the center is set but still slightly jiggly. Once done, turn off the oven and leave the cheesecake inside with the door ajar for 10 minutes. This gentle cooling helps prevent cracks. Afterward, let the Carrot Cake Cheesecake cool completely at room temperature before refrigerating for at least 4 hours or overnight.

While the cheesecake cools, prepare the optional cream cheese frosting. In a mixing bowl, beat softened cream cheese and unsalted butter together until creamy. Gradually add powdered sugar and a splash of vanilla extract, mixing until the frosting is light and fluffy. Once the Carrot Cake Cheesecake is chilled, you can spread this decadent frosting over the top for added indulgence.

Carefully remove the Carrot Cake Cheesecake from the springform pan, allowing it to sit for a moment before slicing. Serve each slice garnished with a sprinkle of cinnamon or chopped nuts for an extra touch.