Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan with butter or cooking spray.

In a large mixing bowl, combine granulated sugar and flour, add softened cream cheese, and blend until smooth. Incorporate eggs one at a time, then stir in sour cream.

In another bowl, whisk together the dry ingredients. In a separate large bowl, mix the wet ingredients before gradually adding the dry mixture.

Pour half of the carrot cake mixture into the greased springform pan. Spread evenly, then dollop and spread one-third of the cheesecake mixture on top. Layer remaining carrot cake mixture and finish with the remaining cheesecake mixture.

Bake for about 60-65 minutes until the center jiggles slightly. Let it cool in the pan on a wire rack.

Cool for 1 hour at room temperature, then refrigerate for at least 6 hours or overnight.

Prepare the topping by mixing softened cream cheese and butter until smooth, then add powdered sugar, sour cream, and vanilla, whisking until fluffy.

Spread the topping evenly over the cheesecake. Sprinkle with chopped pecans if desired. Chill again before serving.