Prepare. Preheat the oven to 175°C (350°F), top and bottom heat. Grease a 23 x 23 cm square tin or line it with baking parchment, leaving an overhang on two sides for easy lifting.
Macerate the plums. Toss the quartered plums with the sugar and lemon juice in a bowl. Set aside while you make the batter.
Make the batter. Beat the soft butter, sugar, vanilla extract and salt until pale and creamy. Add the eggs one at a time, beating well after each. Sift the flour with the baking powder and fold it in alternately with the milk until you have a smooth batter.
Spread. Spread the batter evenly into the prepared tin. It will look like a thin layer — this is correct.
Arrange the plums. Place the plums closely over the batter, slightly overlapping, cut side facing up.
Make the streusel. Rub the flour, sugar, vanilla sugar, cold butter and salt together quickly with your fingertips until you have uneven crumbs. Scatter evenly over the plums.
Bake. Bake for 45-50 minutes, until the streusel is deep golden and a skewer inserted into a cake-only area comes out clean. If the plums are very juicy, bake 5 minutes longer.
Cool and serve. Let the cake cool completely in the tin before lifting it out and cutting. Dust with powdered sugar just before serving.
