Add banana, brown sugar, and butter to a nonstick pan. Cook over medium heat, stir in the cinnamon and allow it to reduce into a syrup consistency.
Add the water and oats to a saucepan on medium heat and stir until combined. Bring to a boil, then reduce to medium-low and cook, stirring often, for about 10 minutes, until the oats are tender.
Remove from heat; mix the banana mixture with the oatmeal; season with salt.