Lightly grease two baking trays and prepare a paper piping bag.
Cream the butter with the sugar until very soft, light and fluffy.
Place the chocolate in a bowl over a saucepan of hot water.
Heat gently, stirring occasionally, until melted.
Stir the melted chocolate into the creamed mixture, then gradually add and fold in the flour to form a fairly firm dough.
Knead lightly, then wrap the dough in cling film and chill it for 30 minutes, or longer if you have time.
Roll out the dough on a lightly floured board to a rectangle measuring 20 x 30 cm/ 8x12 in, then cut it into smaller rectangles, measuring 5 x 7.5 cm/2 x 3 in.
Transfer the biscuits to the prepared baking trays.
Bake in a moderate oven (180C, 350F, gas 4) for about 18 minutes, or until slightly darkened in colour and cooked.
Remove the hot biscuits from the trays and transfer them to a wire rack to cool completely.
While the biscuits are cooling, make the filling.
Melt 50 g/ 2 oz of the plain chocolate as described above.
Place the butter, icing sugar, melted chocolate and rum into a bowl and beat for 2-3 minutes, or until the mixture is light and fluffy.
Sandwich the biscuits together in pairs with the chocolate filling and placethem on a wire rack standing over a clean baking tray.
To coat the biscuits, melt the remaining plain chocolate and spoon a little over each biscuit.
Smooth it over evenly to cover the surface completely.
Then melt and spoon the milk chocolate into the paper piping bag and snip a small hole in the end.
Pipe a zig zag of milk chocolate down the length of each biscuit.
Allow the chocolate to set before serving the biscuits.