Dissolve the coffee in the boiling water. Beat the butter and sugar together in a mixing bowl until pale and creamy. Add the dissolved coffee then gradually mix in the flour to make a smooth soft dough.
Shape the dough into a log then chill for 15 minutes. Slice the chilled log into 20 pieces. Roll each piece into a ball, arrange on 2 greased baking sheets and flatten slightly by pressing with a fork. Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 8–10 minutes until browned. Leave the biscuits to cool for 5 minutes then transfer to a wire rack to cool completely.
Make the filling. Dissolve the coffee in the boiling water. Beat the butter and icing sugar together then stir in the dissolved coffee until smooth and fluffy. Use to sandwich the biscuits together in pairs. Eat within 2 days.