Prepare the Carrot Cake Layer:

• Preheat the oven to 350°F (175°C). Grease and flour a 9-inch springform pan.
• In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
• In a large bowl, beat together the granulated sugar, brown sugar, and oil until well combined.
• Add eggs one at a time, beating well after each addition. Mix in vanilla extract.
• Fold in the grated carrots and nuts (if using).
• Pour the batter into the prepared pan and spread it evenly.
• Bake for 25-30 minutes or until a toothpick inserted comes out clean. Let it cool completely in the pan on a wire rack.

Prepare the Cheesecake Layer:

• Reduce the oven temperature to 325°F (165°C).
• In a large bowl, beat the softened cream cheese until smooth.
• Add sugar and vanilla extract, and beat until combined.
• Add eggs one at a time, mixing well after each addition.
• Mix in the sour cream until smooth.
• Pour the cheesecake batter over the cooled carrot cake layer in the springform pan.
• Smooth the top with a spatula and tap the pan to remove air bubbles.
• Bake for 50-60 minutes, or until the center is set and the edges are lightly browned. Turn off the oven and let it cool with the door ajar for 1 hour. Cool to room temperature before refrigerating for at least 4 hours or overnight.

Prepare the Cream Cheese Frosting:

• In a medium bowl, beat the softened cream cheese and butter until creamy.
• Gradually add the powdered sugar and beat until smooth.
• Mix in the vanilla extract.
• Add heavy cream or milk as needed to reach the desired consistency.

Assemble the Cake:

• Once the cheesecake is chilled, remove the sides of the springform pan.
• Place the cake on a serving platter.
• Spread cream cheese frosting over the top and sides of the cake.
• Garnish with additional chopped nuts or grated carrots if desired.
• Slice and serve chilled.