Melt butter in non-stick pan. When butter is hot and bubbly, place sliced bananas cut side down in pan and cook over medium high heat. Cook for 3 minutes or until cut side is golden and caramelized. Remove from heat.
Place banana rounds on a parchment lined cookie sheet and place in freezer
After sliced bananas have cooled, slice in half forming 8 quarters. Place on cookie sheet with banana rounds and freeze overnight.
To make gelato, place bananas, vanilla, and rum in the bowl of a food processor fitted with a metal blade and pulse until fully combined and mixture has the consistency of gelato. (Add a couple of ice cubes to the food processor and blend if you want a more icy version.)
Scoop into compote glasses or bowls and garnish with a sprig of mint.