01 - Rinse the short-grain rice thoroughly under cold water until the rinse water is clear. Drain completely.
02 - In a medium saucepan, combine rinsed rice, water, and a pinch of salt. Bring to a gentle simmer over medium heat, then cover and cook for 5 minutes.
03 - Stir in the whole milk, granulated sugar, and vanilla bean seeds or extract. Return to a gentle simmer, stirring occasionally.
04 - Reduce heat to low and cook uncovered, stirring frequently until the rice is tender and the mixture achieves a creamy consistency, approximately 25 to 30 minutes. Remove from heat and allow to cool slightly.
05 - In a mixing bowl, whisk together chestnut purée, heavy cream, powdered sugar, vanilla extract, and rum (if using) until smooth and fully blended.
06 - Spoon rice pudding into serving bowls or glasses, topping each with a generous layer of chestnut cream. Garnish with chopped candied chestnuts and a pinch of cinnamon as desired.
07 - Serve immediately while warm or refrigerate for a firmer texture according to preference.