Put the rice to boil with 1 cup of water until the liquid is absorbed. Pour in the milk and sugar while stirring gently. Bring to a boil for 10 min, then slowly add, with stirring again, the starch, egg yolk and a little less than 1/2 cup of water.
Stir until boiling and boil for 5-10 minutes. Then add the vanilla and distribute the mixture into oven-safe bowls. To each, add a little water.
Arrange the bowls in a baking dish in a water bath in a moderately preheated oven. Bake until they get a dark brown crust.
Once removed from the oven, cover them with plates on top. Serve cooled.