I have made this pudding for several years. It is so creamy and rich it is hard to stop eating. This recipe is quite variable as it is equally as good without the sauce. You can also omit the cream cheese to make a less rich pudding.
Combine 3-1/2 cups of the milk with rice, sugar, and salt in saucepan. Bring to a boil over medium heat and cook for about 15 minutes stirring occasionly. It should be thick and creamy. In a mixing bowl, beat cream cheese and eggs together with remaining milk. Stir into rice mixture and cook for another 2 minutes, stirring constantly. Remove from heat and add 1 teaspoon of the vanilla. Divide into dessert bowls to chill.
Drain the pineapple. Combine the reserved pineapple juice with brown sugar, cornstarch, butter, and salt in saucepan. Bring to a boil and cook for 2 minutes or until thickened. Stir in the remaining vanilla and the pineapple. Spoon over pudding.