Preheat the oven to 350°F. Lightly spray a 9-inch springform pan with nonstick spray. Set aside.
In a medium bowl, combine the flour, corn starch, baking powder, baking soda, cinnamon, nutmeg, ginger, and nuts, then set aside.
1 cup all-purpose flour, 1 tablespoon cornstarch, 1 teaspoon baking powder, ½ teaspoon baking soda, 1 teaspoon cinnamon, ¼ teaspoon nutmeg, ¼ teaspoon ginger, ⅓ cup chopped walnuts
In a large mixing bowl, whisk together the oil, sugar and eggs. Whisk together until they are well combined.
½ cup vegetable oil, ½ cup granulated sugar, 2 large eggs
Using a large spoon or spatula, stir in the shredded carrots. Then gradually add in the flour and spice mixture, until the batter is mixed together and thick.
1 cup shredded carrot
Pour the batter into a 9 inch springform pan, very lightly sprayed or buttered at the bottom and on the sides of the pan.
Bake for about 18-20 minutes until the top of the cake springs back to the touch.
While the cake is baking, prepare the cheesecake filling.
In a large bowl, beat the cream cheese until it is smooth and creamy, removing all clumps. Add in the sour cream, sugar, eggs, and vanilla.
24 ounces cream cheese, ½ cup sour cream, ⅔ cup granulated sugar, 2 large eggs, 1 teaspoon pure vanilla extract
Continue mixing for about two-three additional minutes, until all ingredients are combined and the filling is smooth and creamy.
Pour the cream cheese filling over the carrot cake. Cover the bottom of the springform pan with foil, and place the pan in a water bath. (I used a cake pan Be sure the water surrounds the sides of the springform pan no more than half way)
Lower the temperature to 325 degrees
Bake the cheesecake for about 50-60 minutes. The cheesecake will still be a little jiggly in the middle, but will have a set top.
Allow the cheesecake to cool to room temperature, and then place in the refrigerator until it is completely chilled and set, 6-8 hours.
To frost the cheesecake, Beat together the cream cheese, butter, powdered sugar, and vanilla. Spread over the top of the cheesecake layer. See note about thickness.
4 ounces cream cheese, 4 tablespoons unsalted butter, 1½ cups powdered sugar, 1 teaspoon pure vanilla extract