Add the water, milk, and a pinch of salt to a large pot over medium-high heat and add the cornmeal very slowly while whisking vigorously.
Keep cooking the cornmeal over medium-high heat, whisking continuously, until the milk starts simmering and the mixture is thickened, just about 5-7 minutes.
Lower the heat to low, cover the pot, and simmer the polenta for 15-20 minutes, stirring every couple of minutes to make sure it doesn’t stick to the bottom of the pot. When the polenta thickens, it’s easier to stir with a wooden spoon or a heat-resistant spatula than with a whisk. While the polenta is simmering, you can prepare the toppings (see below).
Once the polenta is cooked, add butter and parmesan. Stir and take it off the heat. Cover it for a couple minutes then taste and adjust the seasoning, adding salt to taste. When it’s time, spoon the creamy polenta into bowls or deep plates, with the toppings below.