Rinse the rice once, then spread it on a clean kitchen towel and pat dry so it toasts rather than steams.

Place the dried rice in a cold 3-quart heavy-bottomed saucepan. Set the heat to medium and toast the rice, stirring occasionally, for 4 to 5 minutes until the grains are faintly golden and smell nutty like popcorn.

Slowly pour the warm milk into the pan - it will steam vigorously at first. Add the vanilla bean pod and its scraped seeds (or vanilla extract), sugar, and salt. Stir to combine.

Bring the mixture to a gentle simmer over medium-low heat. Once bubbling, reduce heat to low and cook uncovered, stirring every 2 to 3 minutes, for 30 to 35 minutes until the rice is tender and the mixture has thickened to a loose, creamy consistency.

While the rice finishes cooking, melt the butter in a small skillet over medium heat. Swirl the pan frequently for 2 to 3 minutes until the butter foams, then turns golden and smells like hazelnuts. Remove from heat immediately.

Stir the heavy cream into the pudding and remove from heat. Discard the vanilla pod. Stir in the brown butter.

Spoon the pudding into bowls. It should look slightly loose - it thickens as it cools. Finish each bowl with a pinch of flaky sea salt if using, and serve warm.