Butter the bottom and insides of a 9-inch spring-form pan and wrap the outside with heavy duty foil (make sure it is waterproof). Take a pan big enough for the spring-form pan to fit down into and place this pan onto the middle rack in your oven and when ready to bake, set spring-form pan in the center of it.
Blend 1 package of cream cheese and 1/3 cup sugar and cornstarch in mixing bowl on low until creamy, scraping down the bowl a couple of times. Blend in the remaining cream cheese 1 package at a time, scraping down the bowl after each addition.
Increase mixing speed to medium and beat in the remaining 1 cup of sugar, then the vanilla and then blend in eggs 1 at a time, beating well after each addition so mixture does not separate. Beat in cream, just until it is mixed.
Gently spoon batter into spring-form pan and then place it into the water pan in the over and add hot water so that the water comes up about 1" up the sides of it.
Bake at 350 until the edges are light golden brown and the top is golden tan, about 1-1/4 hours. Remove from the water bath and cool spring-form pan on wire rack for 2 hours, then cover with plastic wrap and refrigerate while still in the pan for about 4 hours, until completely cold. I put it in the freezer about 1 hour before assembling the cake. Remove the sides and run a long spatula under the cake to separate from the bottom. Dip the spatula in hot water and dry it off first to make it easier. (I have an electric oven and turn on the burner until barely warm and then sit the pan on the burner a minute or 2 until it removes easily from the bottom pan).
2Carrot Cake Layers, Top and Bottom of Cake:
Preheat oven to 325 degrees.
Sift together dry ingredients 2 or 3 times. Generously butter and then flour bottom and sides of two 9" cake pans. Also line the bottom with parchment paper, don't let the paper go up the sides of the pan.
Combine all of the cake ingredients in a bowl and beat 4 or 5 minutes. Divide evenly between the 2 pans and bake, checking first at 45 minutes and keep baking until you can stick in a wooden pick in the middle and pull it out without wet batter on it. There will be a few little crumbs.
Place pans on wire racks, turning cake out onto wire racks to cool completely. These layers must be completely cool. You may let them sit in the freezer about 15 minutes once they are cool before assembling.
3The Fourth, Outside "Layer" (Frosting):
Beat softened (important) cream cheese and butter together until creamy and add powdered sugar until the correct consistency for frosting the cake and then add vanilla (I also add about 1/4 tsp salt, just for flavor).
Place one layer of cake on bottom of large cake plate or stand. Frost the top of that layer and then place the 2nd layer, the cheesecake, but do not frost the top of the cheesecake. Place the 3rd layer, the remaining carrot cake layer, and then generously spread the "4th layer", the icing, over top and sides of cake.