In a medium saucepan, combine the rice, water, and salt.
Place on medium-high heat and bring to a simmer, then cover and cook until the water has been absorbed, about 15 minutes.
Add the milk, sugar, and cherries. Cook uncovered for about 30 to 40 minutes, stirring frequently to keep the rice from sticking to the bottom of the pan. When the pudding is done, the rice and milk should form a thick porridge and the rice should be tender but still have a slight bite.
When done, remove from the heat and add the vanilla. Serve warm, with chocolate shavings.