Step 1: Prepare the Polenta

1. Boil the Liquid: In a medium-sized pot, bring 4 cups of water (or a mixture of water and milk for creamier results) to a boil. Add the salt to the water.
2. Add the Cornmeal: Gradually whisk in the cornmeal, ensuring there are no lumps. Lower the heat to a simmer once all the cornmeal is added.
3. Cook the Polenta: Stir frequently with a wooden spoon to prevent sticking, cooking for about 20-25 minutes or until the mixture thickens and the grains are tender.
4. Incorporate Butter and Cheese: Stir in the butter and Parmesan cheese until fully melted and incorporated. Taste and adjust seasoning if necessary. Cover and set aside to keep warm.

Step 2: Poach the Eggs

1. Prepare the Water: Fill a medium saucepan with water and bring it to a gentle simmer. If desired, add white vinegar to the water to help the eggs hold their shape.
2. Crack the Eggs: Crack each egg into a small bowl or ramekin to ensure the yolk stays intact.
3. Poach the Eggs: Create a gentle whirlpool in the simmering water using a spoon, then slide one egg into the center. Let it cook for 3-4 minutes, until the white is set but the yolk remains runny. Use a slotted spoon to carefully remove the egg and set it on a plate. Repeat with the remaining eggs.

Step 3: Assemble the Dish

1. Divide the creamy polenta among four bowls.
2. Top each bowl with a poached egg.
3. Garnish with your choice of toppings, such as fresh herbs, black pepper, or sautéed vegetables. Serve immediately.