Step 1

Measure out the rice and milk. 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.

Step 2

Add the flavorings. 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.

Step 3

Bring to a simmer. 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.

Step 4

Simmer until the rice is tender. 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.

Step 5

Add the butter and vanilla extract. 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.

Step 6

Serve the rice pudding. The rice pudding will continue to thicken as it cools. Thin out with more milk if desired, and serve warm or cold.