Preheat the oven to 350°F (175°C) and grease a 9-inch springform pan, lining the base with parchment paper.

In a mixing bowl, beat together cream cheese and granulated sugar until smooth, then mix in sour cream, heavy cream, and vanilla extract. Add eggs one at a time.

In a separate bowl, sift together flour, baking powder, baking soda, salt, and ground spices. In another bowl, combine oils and brown sugar until fluffy, then stir in grated carrots and wet ingredients, folding in the dry mixture until combined.

Pour half of the carrot cake batter into the springform pan, add dollops of cheesecake batter, repeat with remaining batters, creating marbled layers.

Bake for 45-55 minutes until the center jiggles slightly, turn off the oven and leave the door ajar for 10 minutes.

Cool the cheesecake at room temperature, then refrigerate for at least 6 hours overnight.

For the frosting, beat cream cheese and butter until smooth, add powdered sugar and vanilla extract until light and fluffy.