In a heavy-based saucepan, heat the oil (use a deep-frying thermometer if you have one) to about 170-180C.
In a medium-sized bowl, whisk together the egg and the milk. In a separate bowl, sift the flour, sugar, baking powder, and salt. Make a well in the centre and add the milk mixture. Mix gently, then add the melted butter and the plums. Mix to combine.
Carefully drop small spoonfuls of doughnut mixture into the dough. Be careful not to overfill the pan, as this will cause the temperature to drop.
Using two spoons, flip the doughnuts to ensure their surface is cooked all over. Cook for about 2 minutes, until golden. Carefully remove, using a spoon, and set aside on a plate lined with paper towels.
To make the glaze, melt the white chocolate, then add the milk and whisk together. Slowly whisk in the icing sugar, adding more icing sugar or milk if necessary to get a good consistency.
When ready to serve, dip the doughnuts into the glaze, sprinkle with freeze-dried plum powder.