Rinse the rice under cold, running water. I like to use a fine-mesh strainer.
Put the water and salt in a pot and bring it to a boil. When it starts boiling, add the rice and the cinnamon sticks. Simmer on medium heat for about 20-25 minutes, stirring occasionally until the rice absorbs the water. After 20 minutes, taste the rice to see if it has cooked through; if it hasn’t, add a little more water and continue to simmer. Do not drain. Continue tasting the rice until it’s done. Then, discard the cinnamon sticks.
Pour ¼ cup of the milk in a bowl. Add the sugar, vanilla, and cornstarch and whisk together. Set aside.
Pour the remaining milk into the rice mixture and turn up the heat to medium-high. Cook for about 2 minutes.
Add the cornstarch mixture and whisk continuously until it thickens, about a minute or so.
Ladle into small bowls.
Press some plastic wrap on the pudding (to prevent a film from forming) and store in the refrigerator.
Or serve immediately with lots of ground cinnamon on top!