Cook oatmeal in a saucepan over medium heat with milk, water, salt, and cinnamon.
Heat a skillet over medium heat, then add butter until melted.
Caramelize bananas and walnuts in butter, adding maple syrup and vanilla.
Separate your egg yolks and whites, setting the whites aside, and whisking the yolks in a small bowl.
Stirring constantly, add a small amount of the oatmeal to the yolks to temper (you want to gently increase the yolks temperature to that of the oatmeal so that they do not cook too quickly, resulting in hard pieces of egg).
Cook on low heat a few minutes more as you stir.
Remove from the stove top and stir a few times to release some of the trapped heat.
Beat egg whites with a hand mixer until fluffy, then fold them into the oatmeal.
Add caramelized bananas and walnuts, leaving a portion for topping.
Notes
Cook time is approximate. Some like their oatmeal softer than others.