Preheat the oven to 350F/180C. Butter a 10" cake pan or a 10" deep pie plate.
In a large bowl mix butter with sugar with a hand mixer until light and fluffy, add an egg and vanilla and continue mixing until well incorporated then add milk, mix for 2 more minutes and set aside.
Sift both flours, baking powder and salt into a medium bowl.
Add the dry mixture to the butter mixture and mix until well combined but do not over mix, about 2 minutes.
Scrape the batter into a buttered dish and level the top.
Scatter blackberries all over the cake batter and bake for 1 hour.
Lightly dust with powdered sugar before serving.