In a saucepan, add rice and water. Bring to a boil. Cover and simmer over low heat until almost all the water has been absorbed.
Add milk and sugar. Mix well.
Over medium heat, bring to a boil. Stirring frequently.
Mix cornstarch with 1/4 cup of milk, then stir it into the pudding. Cook on medium heat until thickened ( while continuously whisking ). Add vanilla extract and stir well. As soon as it starts to boil, add heavy cream. Mix.
As soon as it starts to bubble, remove it from the heat and let it cool slightly—it will thicken further as it rests.
Serve warm or chilled with your favorite toppings.