Mash 1 banana in a small bowl.
Slice 1 banana into ½-inch thick slices.
Heat 1 tablespoon butter in a small saucepan over medium-high. Add 1 tablespoon maple syrup and cook, stirring occasionally until mixture bubbles and starts to turn dark amber brown, about 1 ½ minutes. Add mashed banana and cook 1 minute, stirring constantly.
Stir in 1 cup milk, ¾ cup oats, ½ teaspoon cinnamon, pinch salt, and pinch ginger and nutmeg, if using. Bring to a boil and cook, stirring frequently, 2 minutes.
Stir in 2 tablespoons water and ½ teaspoon vanilla, cover, remove from heat, and let stand 5 minutes.
Meanwhile, heat remaining 2 tablespoons butter and 2 tablespoons maple syrup in a skillet over medium-high until bubbly and starting to turn golden brown. Add banana slices in a single layer, reduce heat to medium, and cook until golden brown and caramelized, about 3 minutes per side.
Divide oatmeal between 2 bowls and top with caramelized bananas.
Top bowls with desired toppings such as toasted and chopped nuts, additional maple syrup, a splash of cream or milk and flaky sea salt.