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Put the butter in a microwave-safe mug and microwave on high for 30-45 seconds until melted. Stir in the caster sugar, flour, baking powder, milk and vanilla until smooth. Microwave on high for 1 min-1 min 15 seconds until cooked through and a skewer inserted into the middle comes out clean. Set aside while you make the icing.
Combine the icing sugar with enough water to create a drizzly consistency, then spoon over the cake (it will melt a little with the heat of the sponge). Scatter over the sprinkles, if using, and serve.