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Preheat the oven to 350°F / 180°C. Grease a 10-inch / 26 cm springform pan and line the bottom with parchment paper.
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Whisk the vanilla pudding powder with the sugar and a little of the milk until smooth.
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Bring the remaining milk to a boil. Whisk in the pudding mixture and cook briefly until thickened. Stir in a pinch of salt.
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Let the custard cool for about 10 minutes. Press plastic wrap directly onto the surface to prevent a skin from forming.
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Mix the flour and baking powder in a bowl.
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Rub the lemon zest into the sugar with your fingers until fragrant.
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Add the lemon sugar, softened butter, and egg to the flour mixture. Knead into a smooth dough.
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Roll out about two-thirds of the dough and use it to line the bottom of the springform pan.
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Use the remaining dough to form a rim around the edge. Prick the base several times with a fork.
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Stir the sour cream and vanilla into the still-warm custard until smooth.
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Spread the sour cream vanilla custard filling over the crust.
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Arrange the raspberries on top. If using frozen raspberries, add them straight from the freezer.
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Bake in the lower third of the oven for about 60 minutes. If the raspberries brown too much, loosely cover the cake with foil.
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The center may still wobble slightly when the cake comes out of the oven. That is normal. It will firm up as it cools.
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Let the cake cool completely, then chill in the refrigerator until fully set, preferably overnight.
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Warm the raspberry jam with lemon juice, rum, or water until smooth.
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Brush the raspberries with the jam glaze before serving.