Preheat your oven to 350°F (175°C) and prepare a 9-inch springform pan. Spray the pan with non-stick cooking spray, ensuring even coverage. Line the bottom with parchment paper.

In a large mixing bowl, beat the cream cheese and granulated sugar together until smooth and creamy, about 2-3 minutes. Gradually mix in the sour cream, heavy cream, and vanilla extract. Add the eggs one at a time.

In another bowl, sift together the all-purpose flour, baking powder, baking soda, salt, and ground spices. In a separate bowl, beat the oil, brown sugar, and granulated sugar together. Mix in sour cream, vanilla, eggs, and grated carrots.

Layer the batters in the prepared springform pan: start with carrot cake batter, then dollops of cheesecake batter, alternating and swirling for a marbled effect.

Bake for 45-55 minutes until the cheesecake jiggles slightly in the center. Watch closely to avoid overcooking.

Cool the cheesecake on a wire rack for about an hour, then cover and refrigerate for at least 6 hours or overnight.

For the frosting, beat the room temperature unsalted butter and cream cheese until smooth. Gradually mix in powdered sugar and vanilla extract until fluffy.

After chilling, remove the cheesecake from the pan and spread the cream cheese frosting over the top. Add a sprinkle of chopped walnuts or pecans if desired.