Make the rice pudding in the morning or a day ahead of time if serving with the warm bananas. Or enjoy it warm or at room temperature with a splash of cold heavy cream.
In a medium saucepan, combine 1 cup milk, cream, vanilla bean, 6 tablespoons sugar, a pinch of salt, cinnamon, and nutmeg. Bring to a boil, then remove from heat, and let steep, covered, for 30 minutes.
Bring a small saucepan of water to a boil; add rice, and blanch for 1 to 2 minutes. Drain, and set aside. Remove vanilla bean and cinnamon stick from milk mixture. Scrape seeds from bean, and stir them back into the mixture; discard bean and cinnamon. Stir in blanched rice; cook, covered, over low heat, stirring occasionally, until liquid is mostly absorbed, about 1 hour.
In a small bowl, whisk together egg yolks and remaining 2 cups milk. Add to rice mixture, stirring well. Cook over medium heat, stirring constantly, until thickened, 10 to 15 minutes. Do not allow to boil. Add 1 tablespoon butter, and stir until melted. Remove pudding from heat, transfer to a bowl, and let cool slightly. Chill in refrigerator, covered, 2 1/2 to 3 hours, or until cold. Pudding will keep, refrigerated, for up to 3 days.
When ready to serve, cut bananas into 1/2-inch-thick diagonal slices. Melt remaining 2 tablespoons butter over medium heat in a heavy skillet. Stir in remaining 3/4 cup sugar and lemon juice, and cook, carefully swirling pan until a golden caramel forms. Add bananas, and cook, stirring occasionally, just until they soften and are coated with caramel, 2 to 3 minutes. Transfer pudding to individual dishes, top with hot bananas, and serve immediately.