Put the cornmeal in a small bowl. Top with 1 cup cold water and stir. Set aside.
In a medium saucepan add the remaining 2 cups cold water and 2 cups whole milk. Bring to a low boil. Add salt and stir. Slowly add the cornmeal and water mixture, using a whisk to stir out any possible lumps.
Once all of the cornmeal is added, turn the flame to low and simmer, stirring frequently, until the polenta has thickened. Depending on the coarseness of your meal, it may take 10-40 minutes. Once thickened, add sugar and vanilla extract. Sprinkle cinnamon in if you life.
Place polenta in small bowls and top with milk and a sprinkle of additional brown sugar if you like.