Combine the milk, rice, and salt in a saucepan over medium heat. Cook at a low simmer, stirring frequently, until the rice is tender, 35 to 40 minutes. In a mixing bowl, combine 1/2 cup sugar, the egg yolks, vanilla, 1/4 teaspoon cinnamon, and the nutmeg. Add this mixture to the rice and cook over medium heat, stirring constantly, for about 4 minutes, or until the mixture thickens. Remove from the heat and let cool.
Mix together 1/2 cup cream, the remaining 1 tablespoon sugar, and the rum, in a mixing bowl. Using a handheld mixer, beat until soft peaks form. Fold into the cooled rice mixture. Refrigerate for 1 hour.
Melt the butter in a skillet over medium-high heat. Stir in the brown sugar, stirring until the sugar dissolves. Add the remaining cinnamon and the bananas. Cook for 1 minute. Remove the pan from the heat and add the liqueur. Place the pan back over the heat and flame the liqueur. Shaking the pan constantly, cook for 30 seconds. Stir in the remaining 1/4 cup cream and remove from the heat. Spoon the banana sauce in each of 4 bowls. Spoon the pudding into the bowls and top with a little more banana sauce. Garnish with confectioners' sugar, ground cinnamon, and cinnamon sticks.