In a small saucepan, combine the water (or milk), mashed banana, and salt. Bring the mixture to a gentle simmer over medium heat, stirring occasionally until the banana breaks down slightly.

Slowly whisk in the Cream of Rice cereal. Continue to whisk continuously for about 1 minute to prevent lumps from forming.

Reduce the heat to low and continue to cook, stirring frequently, for 5-7 minutes, or until the mixture has thickened to your desired consistency. The oatmeal will continue to thicken as it cools.

Remove from the heat and stir in the vanilla extract. Transfer the cream of rice to your serving bowl.

For the topping: In a separate small skillet over medium heat, melt the butter or coconut oil. Add the sliced banana and brown sugar.

Caramelize the banana slices for 1-2 minutes per side until golden brown and slightly softened. Pour the caramelized bananas and any remaining pan sauce over the cream of rice bowl.