Preheat your oven to 350°F (175°C) and grease a 9-inch springform pan with butter.

Blend cream cheese and granulated sugar until smooth. Add eggs, one at a time, mixing well. Include vanilla extract and sour cream.

In a separate bowl, whisk together flour, baking soda, baking powder, and salt. Mix wet ingredients until smooth and fold in dry mixture and grated carrots.

Layer 1.5 cups of carrot cake batter in the prepared pan, followed by 1/3 of the cheesecake mixture. Repeat two more times, ending with cheesecake.

Bake for 60-65 minutes, covering with foil after 40 minutes. The center should jiggle slightly.

Cool in the pan for 1 hour, then refrigerate for at least 6 hours, preferably overnight.

Beat cream cheese and butter for the topping until fluffy. Add powdered sugar, sour cream, and vanilla extract, mixing until creamy.

Spread topping over the chilled cheesecake and sprinkle with chopped pecans if desired. Chill briefly before serving.