Bring the double cream, water, brown rice and salt to the boil in a pot; reduce heat to low, cover and simmer until the liquid is completely absorbed, about 80 minutes. Fold the sultanas or raisins into the mixture and continue cooking until they plump, about 10 minutes more.
Whisk the egg yolks, sugar and cinnamon together in a bowl; slowly pour into the pot with the rice whilst stirring. Cook and stir until the mixture thickens, about 6 minutes. Remove from heat and stir in the butter and vanilla extract.