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

In a large mixing bowl, whisk together granulated sugar and all-purpose flour. Blend in softened cream cheese until smooth, then add eggs one at a time, followed by sour cream.

In a separate bowl, whisk together baking powder, baking soda, ground cinnamon, and nutmeg. In another bowl, mix canola oil and unsweetened applesauce, then combine with the dry ingredients and fold in grated carrots.

Pour half of the carrot cake mixture into the pan, then add a layer of cheesecake mixture. Top with the remaining carrot cake batter and drizzle the leftover cheesecake on top.

Bake for 60-65 minutes until set but jiggly in the center. Tent with foil after 40 minutes to prevent browning.

Let cool on a wire rack for 1 hour, then refrigerate for at least 6 hours.

Whip together cream cheese and butter for the topping, gradually adding sifted powdered sugar until creamy. Spread over the chilled cheesecake.

Refrigerate for another hour. Optionally garnish with chopped pecans before slicing and serving.