In a large pot, add the milk and vanilla. Stir frequently over medium heat to prevent a skin from forming.
Once the milk is heated, reduce the heat to medium-low, add the rice, and stir.
Continue stirring every 2–3 minutes to prevent a skin from forming and to ensure even cooking.
As the mixture thickens, stir more frequently. The rice should be fully cooked in about 30-45 minutes (taste to check for doneness).
Once the rice is tender, remove the pot from heat and stir in the sugar.
Transfer the mixture to a large bowl, cover, and refrigerate for at least 4 hours (or until fully cooled), preferably overnight.
Before serving, whip the heavy cream to soft peaks, then gently fold it into the chilled rice pudding.