Preheat the oven to 350 F, and line an 8x10-inch baking tray with baking paper.
Whisk the butter and sugar together until the mixture is pale and creamy.
Add the three eggs, the vanilla extract, and the yogurt to the mixing bowl, and combine nicely, stopping to scrape down the sides of the bowl part way through to make sure that everything is mixed.
Mix the ½ teaspoon of baking powder into the ¾ cup of self-rising flour. Then, add this to the mixing bowl and mix together until well combined.
Add the final tablespoon of flour to the blackberries, and coat them well. This will stop the blackberries from bleeding into the batter.
Spread a thin layer of batter on the bottom of the cake pan, and then dot half of the blackberries on top. Finish by spreading the rest of the batter over this, and put the rest of the blackberries on the top layer.
Sprinkle the top of the cake with the sugar nibs, and then bake in the oven for 30 to 35 minutes, or until the sponge springs back to the touch.
Allow the cake to cool for 15 minutes before cutting and serving alongside fresh blackberries, cream, or vanilla ice cream.