Grease a 9 or 9 1/2 inch springform pan. Set aside. (I used a 10" pan so my baking time was slightly reduced)
In the large bowl of an electric mixer, beat together 2 packages cream cheese and 3/4 cup sugar until smooth. Beat in 1 tablespoon flour, 3 eggs and 2 teaspoons vanilla until smooth. Set aside.
For the carrot cake: In a large bowl, combine oil, 1 cup sugar, 2 eggs and 1 teaspoon vanilla, blending thoroughly. Stir in 1 cup flour, baking soda, cinnamon and pinch of salt, mixing well. Stir in drained pineapple, carrots, coconut and walnuts.
Spread 1 1/2 cups carrot cake batter over bottom of prepared pan. Drop large spoonfuls of cream cheese batter over carrot cake batter. Top with large spoonfuls of remaining carrot cake batter. Repeat with remaining cream cheese batter, spreading evenly with a knife. (Do not marble with the knife.)
Bake in preheated 350˚F oven 50 to 65 minutes or until cake is set and cooked through. Cool to room temperature and then refrigerate. When cake is cold, prepare the frosting.
For the frosting: In a bowl of an electric mixer, combine 2 ounce cream cheese, butter, powdered sugar, 1/2 teaspoon vanilla, 1 tablespoon reserved pineapple juice and a dash of salt. Beat until smooth and of spreading consistency. Frost top of cheesecake. Refrigerate 3 to 4 hours before serving.