Preheat your oven to 350°F (175°C) and prepare a 9-inch springform pan by greasing it with baking spray and lining the bottom with parchment.

In a large mixing bowl, beat the cream cheese and granulated sugar on high for about 2 minutes, scraping down the sides halfway through. Add in the sour cream, heavy cream, and vanilla extract, mixing until completely smooth. Incorporate the eggs one at a time on low speed, ensuring each one is well combined before adding the next.

In a separate mixing bowl, sift together the all-purpose flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger. In another large bowl, beat the oil, brown sugar, and granulated sugar on high for 1 minute until fluffy. Add the sour cream, vanilla, grated carrots, and eggs, mixing until just combined. Gradually add the dry ingredients on low speed.

Spoon half of the carrot cake batter into the prepared springform pan, spreading it evenly. Dollop about a third of the cheesecake batter over the carrot cake layer. Repeat this process by pouring in the remaining carrot cake batter followed by the rest of the cheesecake batter.

Place the springform pan in the preheated oven and bake for 45-55 minutes until the edges are set and the center has a slight jiggle. Remove from the oven and let it cool completely on a wire rack before transferring to the fridge. Chill for at least 6 hours, or overnight if possible.

Sift the powdered sugar in a bowl to eliminate lumps. In a mixing bowl, beat the softened unsalted butter and cream cheese on high for about 2 minutes until smooth and creamy. Gradually add the sifted powdered sugar and vanilla, mixing until everything is blended.

Once the Carrot Cake Cheesecake is fully chilled, gently release it from the springform pan. Spread a generous layer of cream cheese frosting on top, smoothing it out with a swirl. Garnish with crushed nuts or a sprinkle of cinnamon if desired. Slice and serve chilled.