Preheat oven to 350°F. Spray a 9-inch springform pan with baking spray, line bottom with parchment paper, and spray again.
For the cheesecake: Beat cream cheese and sugar on high for 2 minutes. Add sour cream, heavy cream, and vanilla; mix on medium until smooth. Add eggs on low just until combined. Set aside.
For the carrot cake: Whisk flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger. In separate bowl, beat oil, brown sugar, and granulated sugar for 1 minute. Add sour cream, vanilla, grated carrots, and eggs; mix until combined. Add dry ingredients on low just until incorporated.
Spread half of carrot cake batter in pan. Dollop 1/3 of cheesecake batter on top. Add half of remaining carrot cake batter in dollops, then another 1/3 of cheesecake batter. Top with remaining carrot cake batter, then finish with remaining cheesecake batter. Do not swirl.
Bake 45-55 minutes until edges are set and center has slight jiggle. Cool completely on wire rack. Refrigerate covered for at least 6 hours or overnight.
For the frosting: Beat butter and cream cheese on high for 2 minutes. Add powdered sugar on low until combined, then vanilla. Beat on high until creamy. Spread over chilled cheesecake.
