For the sheet cake with blackberries, beat yogurt, granulated sugar and eggs until very fluffy. Add vanilla sugar and continue to beat until fluffy. Pour in the oil and stir it in.
Mix the baking powder into the flour and gently stir everything in. Spread the mixture on a greased baking sheet and top the sheet cake with fruit. Bake for 25-30 minutes at 170 degrees with hot air.