Bring milk, water, salt, and butter to a boil, stirring often so milk doesn’t scald.
On a low heat, add polenta, stirring continuously. Add more water depending on desired creaminess. Take off heat and add Parmesan cheese.
Heat olive oil in a skillet. Add onions and sauté for about 3 minutes or until soft. Add spinach. Cook until spinach is wilted. Add garlic and balsamic vinegar. Mix well. Remove spinach and onions with a slotted spoon or tongs. Fry eggs in remaining liquid. Add salt and pepper to taste.
Spread half of polenta on a plate. Spoon on half of spinach/egg mixture and then top with an egg. Repeat on other plate.