In a small saucepan, heat water to boiling, and, stirring constantly, slowly add Cream of Rice. Return to boiling, and reduce heat to simmer. Continue to cook 30 seconds, stirring constantly. Remove from heat, cover and let stand 1 minute.
Meanwhile, whisk egg in a small bowl. Once Cream of Rice is cooked, whisk 2 tablespoons cooked cereal into the egg, then slowly whisk egg mixture into saucepan of cooked cereal.
Add cinnamon and honey, and simmer an additional 2 minutes. Stir in vanilla. Carefully pour breakfast pudding into a serving bowl. Top with walnuts, sliced banana, and additional cinnamon if desired.