Combine the milk, water, salt and cornmeal in a 2 or 3 quart heavy bottomed saucepan. Stir with a fork to eliminate lumps. Heat just to a boil (but without scorching). Reduce heat to low and simmer for 25 minutes, stirring occasionally with a wooden spoon. If, near the end of cooking, the polenta is becoming to thick and heavy to stir, add 1 or more tablespoons cold water to loosen the mixture enough to be able to stir it and maintain a creamy consistency..
Remove from the heat. Add butter, 1/4 cup Parmesan, and the herbs, and stir quickly to incorporate. Pour the still-hot polenta into a buttered cake pan and smooth evenly with a spatula. Cool thoroughly until firm before cutting into serving portions. If prepared ahead of time, the polenta can be covered and refrigerated, uncut, for several hours or overnight.
To toast the polenta, turn it out of the pan and cut into the desired serving size and shape. Place the pieces on a sheet pan, sprinkle with remaining Parmesan and place in a 375 degree oven for 10 minutes. If the top has not browned sufficiently, toast under the broiler briefly before serving.