In a pot, place the rice, milk, water, heavy cream and butter over medium heat and let it come to a boil.
Once boiling, lower heat and cover, simmer for 20-25 minutes. The rice should be just about cooked but you should have some liquid left, if not add a small amount if milk.
Remove from heat. Add can of sweetened condensed milk. Stir. Add vanilla, cinnamon, salt.
Return to heat and cook for 5 minutes.
Remove from heat and add egg- stirring constantly.
Serve warm or chill in a bowl in the refrigerator