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. 
3 cups milk 
1 cup heavy cream
1 vanilla bean, split 
3/4 cup plus 6 T's sugar 
1 pinch of salt 
1 cinnamon stick 
1 pinch nutmeg 
1/2 cup long ~ grain white rice 
2 large egg yolks 
3 T's unsalted butter 
3 ripe, but firm medium bananas 
1 tsp. freshly squeezed lemon juice 
In a medium saucepan, combine 1 cup milk, cream, vanilla bean, 6 Ts sugar, a pinch of salt, cinnamon and nutmeg. Bring to a boil, then remove from heat, and let set, 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 T 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 Ts 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.