Cheesecake Layer:
Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
In a mixing bowl, beat the cream cheese and sugar until smooth.
Add the eggs one at a time, mixing well after each addition. Stir in the sour cream and vanilla extract.
Pour the cheesecake batter into the prepared pan and bake for 35-40 minutes, or until set but slightly jiggly in the center.
Cool completely and refrigerate for at least 4 hours or overnight.
Carrot Cake Layer:
Preheat your oven to 350°F (175°C). Grease and line a 9-inch round cake pan with parchment paper.
In a bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
In a separate bowl, whisk together the oil, sugar, egg, and vanilla extract until smooth.
Gradually mix the dry ingredients into the wet ingredients until combined. Fold in the grated carrots and nuts, if using.
Pour the batter into the prepared pan and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Cool completely on a wire rack.