In a medium saucepan, bring 4 cups of water or vegetable broth to a gentle simmer over medium heat. Gradually whisk in 1 cup of polenta, stirring constantly to prevent lumps. Reduce the heat to low, and continue cooking for about 20-25 minutes.

Once your polenta is perfectly cooked, stir in ½ cup of milk or cream, followed by 2 tablespoons of butter until fully melted. If using, mix in ½ cup of grated Parmesan cheese. Season with salt and black pepper to taste.

While your polenta is cooking, fill a separate saucepan with water and bring it to a gentle simmer. Add 1 tablespoon of white vinegar to the water. Crack each egg into a small dish, then gently slide them into the simmering water. Poach the eggs for 3-4 minutes.

To serve, spoon creamy polenta into bowls, top with poached eggs, and garnish with fresh parsley or chives if desired. Serve immediately.