Bring the water and 1 tablespoon of salt to a boil in a large saucepan. Slowly whisk in the cornmeal, then reduce the heat to low. Cook for 15 to 20 minutes, stirring often, until the polenta thickens. Remove from the heat and stir in the cheese, milk, and butter. Season with salt and pepper, to taste.
Meanwhile, heat the olive oil in a medium skillet over medium heat. Add the onions and cook for 4 to 5 minutes, until softened. Add the maple syrup and cook for another 5 to 6 minutes, stirring often, until the onions are tender and lightly caramelized. Transfer the polenta to bowls and top with the maple onions.