Boil the semolina with a little sugar. Make a mixture from the flour, semolina, sugar, baking powder and vanilla and leave it aside.
In a buttered baking dish, pour in 1/3 of the dry mixture, and on it place banana mixture. Keep alternating between the mixtures until you run out of them.
Top with melted butter and put to bake until lightly tanned in a moderate oven.
If you'd like to make this dessert into a cream instead, mix all the products in a pot on the stove. Distribute the cream into separate bowls and let it cool for a good few hours in the refrigerator. If desired, add a few ladyfingers or biscotti in each bowl.