In a medium saucepan heat the rice, milk, sugar, salt, and butter over medium heat. Stir until the milk begins to simmer, with small bubbles around the edges.
2 cups cooked rice, 2 cups milk, 1/3 cup granulated white sugar, Pinch of salt, 1 tablespoon unsalted butter
Reduce the heat to low and continue to stir.
Cook until the rice pudding is thickened, about 15 to 20 minutes. Stir in the vanilla.
1/2 teaspoon vanilla
Serve the rice pudding warm or transfer it to the refrigerator. It will keep, covered, in the refrigerator for several days.
Notes
To make the chocolate version, follow the recipe card, using 2 cups Dark Chocolate milk instead of plain milk and 1 teaspoon espresso powder (added while cooking the rice). Bump up the chocolatey-ness by tossing ½ cup chocolate chips in, after allowing the rice pudding to cool a bit (so they stay as chips rather than totally melting into the pudding).