Place 16 mini silicone muffin cases on a baking sheet.
Put the butter, sugar, flour and egg in a bowl and beat with a hand-held electric whisk until light and creamy. Stir in the chopped nuts. Divide among the cases.
Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 10–12 minutes, or until risen and just firm. Leave in the cases for 2 minutes then transfer to a wire rack to cool completely.
Make the frosting by heating the butter, sugar and milk in a saucepan until the sugar dissolves. Bring to the boil and boil for 1 minute until the mixture turns slightly syrupy. Remove from the heat and pour into a bowl. Sift the icing sugar into the bowl and beat until the mixture is smooth and fudge like.
Spread over the tops of the cakes with a palette knife and scatter with chopped peanuts.