Bring oats, water, milk, salt, and a third of the sliced bananas to a boil in a medium saucepan. Reduce heat, cover, and let simmer on very low heat for 20–25 minutes for rolled oats, and 30–35 minutes for steel-cut oats. Stir occasionally.

Meanwhile, melt butter in a large nonstick skillet over medium-low heat. Add remaining bananas and sprinkle with brown sugar, nutmeg, and cinnamon. Cook until caramelized, stirring often, about 5 minutes. Gently stir in walnuts. Divide oatmeal into bowls and top it with caramelized banana and walnut mixture. Serve immediately.