In a saucepan, add the rice and water and bring to a boil. Lower the heat and cook, covered, for about 25 minutes.
Add 4 cups of milk, the heavy cream, and sugar. Bring to a boil. In the meantime, dissolve the cornstarch in the remaining milk. Now gradually add it, stirring constantly, to the rice mixture. Add the salt and vanilla extract.
Simmer uncovered, on a low heat, and stirring frequently, for about 15 minutes. When done, divide between individual ovenproof dishes (I used ramekins) and let cool to a room temperature.
Sprinkle lightly with sugar and place in the oven under the broiler until the surface is lightly browned. Sprinkle with some cinnamon and serve right away or let cool and refrigerate until chilled. In this case, sprinkle with cinnamon before serving. Enjoy!