Preheat oven to Gas Mark 4, 180°C, fan 160°C. Line baking trays with nonstick baking paper.
Place the butter and sugar in a bowl and beat until light and fluffy. Beat in the egg until smooth, then stir in the flour, bicarbonate of soda, baking powder and a pinch of salt. Add the milk and vanilla and stir to combine.
Using an ice cream scoop, place spoonfuls on a tray, well spaced apart, and bake for 15 minutes until golden brown and just firm to the touch. Leave on the tray for 5 minutes before removing to cool.
To make the buttercream, place the butter in a bowl with ½tsp of boiling water. Add the icing sugar and beat until smooth. Use to sandwich the whoopie halves together.
To make the glacé icing, mix the icing sugar with ½tsp water to make a very thick, pourable icing. Drizzle over the whoopies.
Dust a work surface with icing sugar and roll out the ready-rolled icing thinly. Cut out snowflakes with a cutter to decorate the whoopies with.