Start by thoroughly rinsing the rice under cold water. In a pot, bring the water to a rolling boil. Add the rinsed rice to the pot, then immediately reduce the heat to low. Cover the pot with a lid, leaving a small gap to allow steam to escape, and cook the rice until all the water is absorbed.

Once the rice is nearly fully cooked—about 90% done—and the water has completely evaporated, take the pot off the heat.

In another pot, combine the milk, sugar, and cinnamon stick. Gently bring this mixture to a simmer, stirring continuously until the sugar fully dissolves.

Carefully incorporate the cooked rice into the simmering milk mixture. Continue stirring constantly as the mixture thickens, which should take around 10 minutes over medium heat. Be mindful not to let the milk scorch; if needed, reduce the heat to medium-low to maintain a steady simmer.

Taste the rice cautiously to ensure it's tender and fully cooked. Once the pudding has thickened to your liking, remove it from the heat. Stir in the pure vanilla bean paste or extract, blending it well into the pudding.

Finally, transfer the pudding into ramekins, glasses, or bowls. You can enjoy it warm, or if you prefer, allow it to cool completely before covering and refrigerating. Whether you like your rice pudding warm or chilled, it's all about personal preference. Enjoy your delicious treat!