Preheat the oven to 325°F (163°C). In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter. Mix until well combined.

Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then remove from the oven and set aside.

In a large bowl, whisk together flour, granulated sugar, brown sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.

Add eggs and vegetable oil, and mix until just combined. Fold in grated carrots and walnuts if using.

Pour the carrot cake batter over the baked crust and spread evenly.

In another bowl, beat the softened cream cheese with granulated sugar and vanilla extract until smooth.

Add eggs one at a time, mixing well after each addition. Stir in sour cream if using.

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

Bake in the preheated oven for 50-60 minutes, or until the cheesecake is set and the edges are lightly browned.

Turn off the oven and leave the cheesecake inside for 1 hour to cool gradually.

Remove from the oven and let cool to room temperature before refrigerating for at least 4 hours or overnight.

Carefully remove the sides of the springform pan. Slice and serve chilled. Enjoy your delicious carrot cake cheesecake!