Grease a fat pan (approx. 32 x 39 cm; at least 3.5 cm deep) and dust with flour. Mix 250 g butter, 275 g sugar, lemon zest and 1 pinch of salt with the whisks of the hand mixer for approx. 8 minutes until creamy.
Stir in the eggs one by one. Mix flour and baking powder, alternating with lemon juice.
Spread the dough on the fat pan and bake in the preheated oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer) for approx. 15 minutes. Let the cake cool down.
1 ¼ Boil up l milk and 150 g sugar. Mix the rest of the milk and pudding powder. Remove the milk from the stove and stir in the pudding powder. Bring to the boil again and simmer for about 1 minute while stirring.
Pour into a bowl and place foil directly on the pudding. Let it cool down.
For the syrup, bring 5 tablespoons of water and 50 g of sugar to the boil in a small pot and let it cool down. Stir rum into the syrup. Place the butter biscuits on a tray with the top side up next to each other and sprinkle with the syrup.
Stir the pudding vigorously. Whisk 400 g butter with the whisk of the hand mixer for about 10 minutes until white and creamy. Stir the pudding into the butter cream by the spoonful.
Cut the cake in half crosswise to make 2 smaller plates. Place on cake plates or trays. Spread both halves of the cake one after the other with plum puree and butter cream and cover with the biscuits.
Finely chop the chocolate and melt it in a small pot with cream while stirring at low heat. Pour into the disposable piping bag and cut off a small corner. Decorate the cake with it in strips.
Chill for about 2 hours.