Transfer the rice, the water, and the salt to a medium sized pot and bring to a boil. Reduce heat to a simmer, cover and cook until all of the water is absorbed (about 15-20 minutes). The rice should be completely cooked through. If not, add 1/4 cup more water and continue cooking.
Add the 2 cups of milk, the sugar, the honey, the cinnamon stick, and the vanilla extract or the vanilla pod (first scrape the seeds from the pod with a knife and add everything to the pot) and cook for another 10 minutes, stirring very often.