Melt the dark chocolate and butter together in a heatproof bowl over simmering water (double boiler method) or in the microwave, stirring frequently until smooth.
In a separate bowl, whisk the egg and powdered sugar together until well combined. Add the vanilla extract and mix.
Gradually stir the melted chocolate mixture into the egg mixture, mixing until smooth and well blended.
Line a loaf pan with parchment paper. Place a layer of tea biscuits at the bottom of the pan.
Pour a portion of the chocolate mixture over the biscuits, spreading evenly. Continue layering biscuits and chocolate mixture until all ingredients are used, ending with a layer of chocolate.
Cover the pan and refrigerate for at least 4 hours or until the cake is set and firm.
Remove from the pan, slice, and serve chilled.