1. Break up the chocolate and place in a bowl over a pan of hot, but not boiling, water. Leave until melted. (Alternatively, place the chocolate in a bowl in a microwave oven and melt on DEFROST.) Stir in the butter.
2. Mix the egg powder, water and rum to a smooth cream. Stir into the chocolate, and beat until thickened slightly and the mixture looks a little grainy. Chill until firm enough to handle.
3. Divide the mixture into 12 equal pieces and roll into balls. Coat with the chocolate vermicelli. Place in paper petit four cases and keep cool.