Heat the oven to 350 degrees F (180 degrees C). Grease a large ovenproof skillet or Dutch oven. Pour in the Medium Ground Cornmeal (1 cup), Water (4 cup), Milk (1 cup), Butter (1 tablespoon) and Kosher Salt (1 teaspoon), and stir with a fork or whisk until blended. The mixture will not look emulsified.
Bake uncovered for 40 minutes. Stir the polenta, taste, add salt if needed, and bake for another 10 to 20 minutes or longer—until it reaches the consistency you like. Remove from the oven, stir, and serve immediately or cover and keep warm until you are ready to serve.
To poach eggs: bring a shallow saucepan filled with water to a boil. Crack Egg (to taste) into individual ramekins or small bowls. Add Distilled White Vinegar (1 splash) to the water. Lower the heat so that the water is barely simmering. Slowly lower each ramekin to the water and pour out each egg. Set a timer for 4 minutes. When the eggs are done, transfer them to a paper towel-lined plate to drain briefly.
To serve: Spoon polenta into bowls. Top with shavings of Shaved Parmesan Cheese (to taste) if desired, and top each mound of polenta with a poached egg. Season with a pinch of Sea Salt (to taste) and Ground Black Pepper (to taste) to taste. Drizzle with Truffle Oil (to taste), if desired. Serve with mushrooms or greens on the side, if desired.