Step 1: Prepare the Carrot Cake Batter

1. Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
2. In a bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt. Set aside.
3. In another large bowl, mix the brown sugar, granulated sugar, and vegetable oil until well combined.
4. Add the egg and vanilla extract, stirring until smooth.
5. Gently fold in the grated carrots and chopped nuts (if using).
6. Gradually mix the dry ingredients into the wet ingredients until just combined. Do not overmix.

Step 2: Prepare the Cheesecake Batter

1. In a large mixing bowl, beat the cream cheese and sugar until smooth and creamy.
2. Add the eggs one at a time, beating just until incorporated. Avoid overmixing to prevent cracks.
3. Stir in the vanilla extract and sour cream, mixing until smooth.

Step 3: Assemble the Layers

1. Pour half of the carrot cake batter into the prepared springform pan, spreading it evenly.
2. Gently spoon half of the cheesecake batter on top.
3. Repeat with the remaining carrot cake batter, then top with the remaining cheesecake batter.
4. Use a knife or skewer to create a slight swirl effect for a marbled look.

Step 4: Bake the Cheesecake

1. Place the pan in the oven and bake for about 50–60 minutes, or until the center is just set and slightly jiggly.
2. Turn off the oven and let the cheesecake cool inside with the door slightly open for 10 minutes.
3. Remove from the oven and let it cool completely at room temperature before transferring to the refrigerator.
4. Chill for at least 4 hours or overnight for the best texture.

Step 5: Prepare the Cream Cheese Frosting (Optional)

1. In a bowl, beat the cream cheese and butter until smooth.
2. Gradually add powdered sugar and vanilla extract, beating until fluffy.
3. Spread a thin layer over the chilled cheesecake or pipe decorative swirls on top.

Step 6: Serve and Enjoy!

1. Carefully remove the cheesecake from the springform pan.
2. Slice and serve with a sprinkle of cinnamon or chopped nuts for extra texture.