Preheat the oven to 180ºC, fan 160ºC, gas 4. Grease a shallow, 1-litre ovenproof tart or flan dish with the butter.
Sift the flour and sugar into a bowl. Whisk in the eggs, one at a time. Slowly add the milk to create a smooth batter. Stir in the sunflower oil and mix well.
Put the blackberries in the base of the dish then pour over the batter. Bake in the centre of the oven for 35-40 minutes, until golden on top and a skewer comes out clean. Dust with icing sugar to serve.