Preheat your oven to 325°F (163°C). In a bowl, beat together cream cheese and granulated sugar until smooth. Add sour cream, eggs, and vanilla extract, mixing until combined.

In another bowl, whisk together flour, baking powder, and cinnamon. In a separate bowl, combine sugar, shredded carrots, chopped pecans, oil, and eggs, then stir in dry ingredients.

Grease a 9-inch springform pan and alternate dollops of the cheesecake and carrot cake batter, creating a marbled effect.

Tent the pan with aluminum foil and bake for 55-65 minutes until the center is slightly jiggly. Cool for an hour, then refrigerate for at least 4 hours or overnight.

Prepare the frosting by beating together cream cheese, butter, powdered sugar, and vanilla extract until smooth. Spread frosting on the chilled cheesecake, sprinkle with chopped pecans, slice, and serve.