Combine 2 packages of cream cheese with 3/4 cup sugar in a large bowl of an electric mixer.
After adding one tablespoon of flour, three eggs, and two teaspoons of vanilla, a smooth batter will result. Prepare a set-aside.
In the meantime, prepare Carrot Cake: Blend oil, sugar, eggs, and vanilla in a large bowl.
As you mix, add one cup of flour, baking soda, cinnamon, and salt, adding a dash at a time.
Adding pineapple, carrots, coconut, and walnuts after draining is optional.Prepare a nine- or nine-and-a-half-inch springform pan by greasing the bottom and spreading 1 1/2 cups carrot cake batter over it. Pour large spoonfuls of the cream cheese batter over the carrot cake batter, and then top with the remaining carrot cake batter.
Spread evenly with a knife the remaining cream cheese batter. Using a knife to marble is not recommended.
Preheat the oven to 350 degrees and bake the cake for 50 to 65 minutes, or until it is set and cooked through.
Refrigerate after cooling to room temperature.
Make Pineapple Cream Cheese Frosting when the cake is cold.
Prepare the filling by combining 2 oz cream cheese with butter, 1 tablespoon reserved pineapple juice, 1 tablespoon powdered sugar, and 1/2 teaspoon vanilla extract.
Spreadable consistency can be achieved by beating until smooth.
Make a frosting topping for the cheesecake.
Before serving, refrigerate it for three to four hours.