Combine the blackberries, raspberries, lemon juice, and sugar in a medium bowl. Stir gently to lightly coat the berries without mashing them. Cover and place in the fridge.
Preheat the oven to 350°F (175°C) and grease a 9-inch (23 cm) springform pan.
In a medium mixing bowl, whisk together the Greek yogurt, eggs, sugar, and vanilla extract. Add the flour, baking powder, and salt, and stir just until combined. Using a spatula, fold in the olive oil until you have a thick, shiny batter.
Pour the batter into the prepared pan and bake for 35–40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow the cake to cool for 10 minutes before removing it from the pan.
To serve the cake, lightly dust the top with powdered sugar and mound the berries on top. Cut the cake into slices and serve with whipped cream, if desired.
