01 -  Thoroughly rinse Japanese short-grain rice under cold running water until the water runs clear. Drain thoroughly. 
 02 -  Place rinsed rice, water, and a pinch of salt in a medium saucepan. Bring to a simmer over medium heat. Cover and cook for 5 minutes. 
 03 -  Add whole milk, granulated sugar, and vanilla bean seeds or extract to the saucepan. Stir to combine and return to a gentle simmer, stirring occasionally. 
 04 -  Reduce heat to low and cook uncovered, stirring often, until the rice is tender and pudding has thickened to a creamy texture, about 25 to 30 minutes. Remove from heat and allow to cool slightly. 
 05 -  In a mixing bowl, combine chestnut purée, heavy cream, powdered sugar, vanilla extract, and rum if using. Whisk vigorously until smooth and creamy. 
 06 -  Distribute warm or slightly cooled rice pudding evenly into serving bowls or glasses. Top each portion with chestnut cream. 
 07 -  Finish with chopped candied chestnuts and a light dusting of ground cinnamon, if desired. Serve immediately or refrigerate for chilled service.