1 cup uncooked short-grain or long-grain white rice, or 3 cups cooked rice
3 to 4 cups dairy or unsweetened non-dairy milk
1/3 cup granulated sugar, plus more as needed
1/4 teaspoon kosher salt
1/2 vanilla bean, or 1 1/2 teaspoons vanilla bean paste or vanilla extract
1 tablespoon unsalted butter (optional)
Add-in options: 1/2 cup raisins, 1/4 teaspoon ground cinnamon
Place 1 cup uncooked short-grain or long-grain white rice, or 3 cups cooked rice in a large saucepan. Add 4 cups milk for uncooked rice, 3 cups milk for cooked rice.
Add 1/3 cup granulated sugar and 1/4 teaspoon kosher salt. If using vanilla bean, scrape the seeds from 1/2 vanilla bean and add the seeds and the pod into the saucepan. If using vanilla bean paste, add 1 1/2 teaspoons. Add any desired add-ins.
Bring the mixture to a vigorous simmer over medium-high heat, stirring frequently and scraping the bottom of the pan with a wooden spoon or rubber spatula so that the rice does not stick.
Reduce the heat to maintain a bare simmer and cook uncovered, stirring occasionally, until the rice is very tender and the mixture starts to thicken, 20 to 22 minutes for uncooked rice, 10 to 12 minutes for cooked rice.
Remove from the heat and stir in 1 1/2 teaspoons vanilla extract if using and 1 tablespoon unsalted butter if desired until melted. Remove the vanilla bean pod if needed. Taste and add more sugar as desired.
The rice pudding will continue to thicken as it cools. Thin out with more milk if desired, and serve warm or cold.