Roll out the short dough 3 mm thick and use it to line the bottom of a tart mould 26 cm in diameter. Chill the dough for several hours, then poke it with a fork at regular intervals and bake for ca. 15 minutes at 170 °C for a golden yellow appearance.
Beat the sponge cake batter, spread it thinly on a baking sheet, bake it, and use a cake ring 24 cm in diameter to cut it into a circular shape. Mash the ripe bananas and combine them with the lemon juice. Spread this banana puree evenly onto the short dough base. Place the sponge cake layer on top and douse it with a mixture of rum and simple syrup.
Dissolve the chocolate over a warm bain-marie. Beat the egg yolks and egg in a food processor. Stir the cold butter into the melted chocolate, and as soon as the butter has fully dissolved, fold in the egg mixture in three steps. Distribute the chocolate mixture evenly over the contents of the tart mould and bake in the oven for 10 minutes at 170 °C.