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Make the shortcrust pastry:
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Mix flour, sugar, and salt in a large bowl. Add butter cubes and rub into the flour mixture until crumbly. Add the egg and quickly knead into a streusel-like dough.
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Use about two-thirds of the dough for the base and sides: Press directly into a greased and parchment-lined 26 cm / 10-inch springform pan (no rolling needed). Form small “sausages” with pieces of dough, press them along the inside edge, and shape into a rim about 3 cm (1 inch) high. Chill the remaining dough in the fridge for later.
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Make the poppy seed pudding filling:
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In a saucepan, whisk together cold milk, pudding powder (or cornstarch substitute), sugar, and poppy seeds. Bring to a boil, stirring constantly, and cook until thickened. Remove from heat, stir in rum if using, and let cool for about 10 minutes.
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Assemble the cake:
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Pour the poppy seed filling into the crust and smooth out. Arrange the quartered plums on top and sprinkle with the brown sugar-cinnamon mix.
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Add the streusel topping:
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Take the reserved dough from the fridge and crumble it evenly over the plums.
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Bake:
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Bake in a preheated oven at 160°C / 320°F (top/bottom heat) for about 60 minutes. The low temperature ensures the crust doesn’t brown too quickly, the filling sets gently, and the streusel turns golden without burning.
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Alternative: Bake at 180°C / 350°F for 45–50 minutes, but cover the streusel with foil toward the end to prevent over-browning.
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Cool & serve:
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Let cool completely before removing from the pan. Serve with whipped cream if desired.