Preheat your oven to 350°F (175°C) and prepare a 9-inch springform pan with non-stick spray and parchment paper.

Beat softened cream cheese and granulated sugar until smooth. Add sour cream, heavy cream, and vanilla extract, mixing until combined. Incorporate eggs on low speed one at a time.

Whisk all-purpose flour, baking powder, baking soda, and salt in one bowl. In another bowl, beat oil and brown sugar, then mix in eggs and grated carrots. Combine dry and wet ingredients gently.

Spoon half of the carrot cake batter into the springform pan, followed by a third of the cheesecake batter. Repeat with remaining batters.

Place the pan in the oven and bake for 45 to 55 minutes, checking for a slight jiggle in the center.

Cool the cheesecake for about 1 hour on a rack. Then refrigerate for at least 6 hours or overnight.

Beat butter and cream cheese until fluffy, then gradually mix in powdered sugar and vanilla extract until smooth.

Remove the cheesecake from the pan and frost the top with cream cheese frosting.