Preheat your oven to 180°C (350°F). Grease a baking dish (approximately 9×13 inches) or line it with parchment paper.
In a large mixing bowl, cream together the softened butter and 160 g of sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla sugar (or vanilla extract) and the yogurt or sour cream.
In a separate bowl, sift together the flour and baking powder. Gradually fold the dry ingredients into the wet mixture until just combined.
2. Assemble the Cake
Pour the cake batter into the prepared baking dish, spreading it evenly with a spatula.
Arrange the halved plums on top of the batter, cut side up, pressing them slightly into the surface.
3. Prepare the Crumble Topping
In a small bowl, combine the 3 tablespoons of flour and 2 tablespoons of sugar. Cut in the 40 g of cold butter with a fork or pastry cutter until the mixture resembles coarse crumbs.
Evenly sprinkle the crumble mixture over the plums and cake batter.
4. Bake the Cake
Bake the cake in the preheated oven for 35-40 minutes, until the top is golden brown and a toothpick inserted into the center comes out clean. If the topping browns too quickly, loosely cover the cake with aluminum foil.
Allow the cake to cool in the pan for about 10 minutes before slicing into squares.
