1. Add rice, water, and salt to saucepan. Cover and cook over lowest flame for about 45 minutes, until grains are broken and falling apart. If the rice starts to stick at any point, add a little more water, ¼ cup at a time and stir.
2. Remove lid from pot, add milk and sugar. Taste, add more sugar as needed. Cover and simmer on lowest flame for another 45-60 minutes, until pudding is creamy and thick.
3. Remove pudding from flame, stir in vanilla.
4. Serve bowls with ground cinnamon on top, or garnished with jam!