In a saucepan, combine the milk, sugar, butter, egg and vanilla using a whisk.
Cook over medium heat, stirring continuously, until the mixture thickens slightly, about 10 minutes.
Take the biscuits and break them into medium-sized pieces and place them in a large bowl. Avoid crushing them into powder.
Pour the chocolate mixture over the broken biscuits.
Mix well until all the biscuit pieces are thoroughly coated with the chocolate sauce.
Transfer the mixture onto a large piece of parchment paper and shape it into a rectangle (or a log if preferred). You can use a spatula or a second parchment paper for shaping.
Wrap the parchment paper tightly around the cake, then wrap it again with plastic wrap to hold the shape.
Place the wrapped cake in the refrigerator and chill for at least 3 hours until it is firm and set. Remove from wrapping and serve.