Carrot cake :
1 cup white flour.
1 teaspoon cinnamon powder.
1 cup of brown sugar.
3 eggs.
1 cup grated carrots.
1/2 teaspoon baking soda, and 1/2 of baking powder.
1/4 cup unsweetened applesauce.
1 teaspoon pure vanilla extract.
1/2 cup vegetable oil.
a pinch o salt.
Cheesecake Mixture :
2/3 cup granulated sugar.
1 1/2 tsp all-purpose flour.
2 large eggs.
1 teaspoon vanilla extract.
1/2 cup sour cream.
2 PKG cream cheese.
For Topping :
1 tablespoon softened butter.
1 cup softened cream cheese.
1 1/4 cups powdered sugar.
1teaspoon vanilla extract.

I preheated the oven to 350 degrees F and prepared a springform pan.

Cheesecake mixture :
I whisked sugar and flour in a large bowl, until well combined.
Using an electric mixer I blended cream cheese and sugar mixture until smooth, I added eggs, vanilla extract, and sour cream, and I blended for 2 more minutes. (set aside ).

Carrot cake :
In a large mixing bowl, I whisked together (for 1 min) white flour, baking soda, baking powder, cinnamon powder, and a pinch of salt.
in another bowl I add oil, applesauce, brown sugar, eggs, and vanilla extract, I blended with a hand mixer, and slowly added dry ingredients, carrots and I mixed very well.
In a greased springform pan, I poured four layers starting by carrot cake mixture then cream cheese mixture, and cake carrots and finally another layer of cream cheese mixture, and baked for 1 hour.
Topping step :
I whipped cream cheese and butter using an electric hand mixer until smooth, I added the remaining topping ingredients and mix again about 5 minutes.
I spread the mixture over the cheesecake and chilled it in the fridge for 1 hour.
P.S: You can add chopped pecans over top.