Place cooked rice, milk, and salt in a small saucepot. Place over medium-low heat, stirring occasionally until thickened, about 10 minutes.
In a small bowl, mix together the beaten egg, heavy cream, cinnamon, and nutmeg, set aside.
Pour sugar into rice mixture, stir to combine. Stream in the heavy cream mixture, stirring constantly until combined. Add both varieties of raisins, and stir to combine. Continue to stir occasionally until thickened, about 5-8 minutes.
When it is thickened, take off the heat and stir in the butter and vanilla. Let cool for 10 minutes, stirring occasionally, serve.