For the banana jam, mash half of the bananas and mix with the lemon juice. Cut vanilla bean in half lengthwise and scrape out the pulp with the back of a knife and add to the lemon juice-banana mixture.
Cut the other half of the bananas into small pieces and stir into the mixture. Bring the banana mixture to a boil in a saucepan and simmer for about 5 minutes. Add the preserving sugar and simmer for another 3 minutes.
Wash out jam jars (3 of them) while hot and pour some rum into the lids. Pour the hot jam into the jars, spread the rum over the jam and seal tightly. Turn jam jars upside down so they stand on the lids and let cool.
Serve the banana jam.
Banana jam goes well with the cakes that are not juicy.