Whisk the flour and cocoa together in a bowl, and make a well in the centre. Pour in the melted butter and mix with a fork until the mixture resembles crumbs. Stir in just enough water to form a soft, smooth dough. Roll the pastry into a ball, wrap in cling film and let rest in the refrigerator for at least 30 minutes.
Roll the pastry out on a lightly floured work surface, and line a buttered tart tin with the pastry base. Pierce with a fork several times, cover with aluminium foil or baking parchment and fill with dry beans.
Bake in the preheated oven until crisp, about 20 minutes. Let cool.
Prepare the filling
Warm the whipping cream in a saucepan until it just begins to simmer. Remove from the heat and stir in the plain chocolate pieces. Cover and let stand for 5 minutes. Beat the mixture with a wooden spoon until very smooth.
Arrange the banana slices in the bottom of the cooled pastry case. Pour the chocolate mixture over the bananas, and cool to room temperature, then place in the refrigerator until the chocolate filling is set, about 1 1/2 hours.
Garnish the tart just before serving with banana slices.