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

Prepare the cheesecake layer by whisking together granulated sugar and flour, then add softened cream cheese and blend until smooth. Introduce eggs one at a time, mixing well, and stir in sour cream.

Tap the bowl lightly on the counter to release air bubbles and set aside.

In a separate bowl, whisk together the dry ingredients for the carrot cake, ensuring even distribution of baking soda and powder.

In another bowl, mix wet ingredients: canola oil, brown sugar, applesauce, and grated carrots until combined.

Fold the wet carrot mixture into the dry ingredients gently until just combined.

Pour half the carrot cake batter into the pan, then spread the cheesecake layer on top, followed by the remaining batter.

Bake for 60-65 minutes, until mostly set with a slight jiggle.

Let cool in the pan for 1 hour, then refrigerate for at least 6 hours or overnight.

Prepare the topping by beating cream cheese and butter until creamy, then add powdered sugar and mix until fluffy.

Spread the topping over the cheesecake and garnish with pecans if desired. Chill for an additional 30 minutes before serving.

Slice and serve with coffee or tea.