Special equipment: A 8-inch square baking dish, preferably not aluminum A hot water bath 20 to 30 spoons, preferably long-handled A kitchen torch*
Preheat the oven to 300 degrees F. Heat the cream, half-and-half, and vanilla bean in a medium saucepan over medium heat just to a boil. Immediately turn off the heat. Set aside to infuse for 10 minutes. Whisk the egg yolks with the sugar in a large bowl just until combined. Whisking constantly, gradually pour in the hot cream mixture. Strain the mixture into the baking pan to smooth it and to remove the vanilla bean.
Place the pan in a hot water bath. Bake in the center of the oven until set but not too firm (it will cook a little more as it cools), 40 to 50 minutes. Remove from the water bath and let cool 15 minutes. Tightly cover with plastic wrap, making sure the plastic does not touch the surface of the custard. (The recipe can be made up to this point and kept refrigerated up to 3 days in advance.) Up to 4 hours before serving, fill your spoons with the chilled cooked custard by scooping each spoon into the pan of custard. Round the tops with a small spatula, or a butter knife. Keep cold. Right before serving, thinly slice the banana (about 1/8-inch thick). Top each spoonful of custard with a slice of banana, lightly pressing it onto the custard. Sprinkle the entire surface with a layer of coarse sugar and place on a baking sheet. Repeat with the remaining spoons. Torch the sugar until it is melted and well browned. Let cool 1 minute before serving.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.