Place a 12-inch saute pan over medium heat. Butter each side of the pound cake slices with 1 1/2 teaspoons of the room temperature butter. Once the pan is hot, place the pound cake slices in the pan, and saute for 1 minute per side. Remove each cake slice to 1 of 4 plates. Wipe out the pan, and return it to the stove. Increase the heat to medium-high and allow the pan to get hot for a minute. Add 2 tablespoons of the cold butter to the pan, when the butter has melted, add the bananas to the pan and saute, stirring often for 1 minute. Add the brown sugar to the pan as well as the cinnamon, nutmeg, vanilla extract and the salt. Continue to cook the bananas for an additional minute, and remove the pan from the heat. Add the rum, ignite with a long kitchen match and let burn until the flame subsides. Return the pan to the stove. Cook the bananas for another 30 seconds before removing them from the heat. Swirl the remaining tablespoon of cold butter into the banana mixture.
To serve, place a scoop of ice cream on top of each slice of sauteed pound cake, and top with equal portions of the flambeed bananas. Garnish with mint leaves and serve immediately.
Combine the half-and-half, vanilla bean and seeds, cinnamon sticks, cinnamon and salt, in a non-reactive saucepan over medium heat. Bring the half-and-half just to a boil to scald it, and remove the saucepan from the heat.
Combine the sugar and egg yolks in a bowl and whisk until pale yellow and thick. Add the half-and-half mixture, about 1/4 cup at a time, to the beaten eggs and sugar, whisking in between each addition, until all is used. Pour the mixture back into the saucepan reduce the heat to medium-low, and cook, stirring, over medium heat, for 5 to 6 minutes, or until the mixture becomes thick enough to coat the back of a spoon. Remove from the heat, strain through a fine mesh sieve and cool completely. Pour the filling into the ice cream machine and follow the manufacturer's instructions for churning time. Place ice cream in a freezer-safe container and freeze until firm, about 8 hours.