Press the plums slightly flat and place them on a plate. Whip 200 g butter with sugar and 1 vanilla sugar in a food processor for 8-10 minutes until thick and creamy. Separate 3 eggs. First stir in egg yolks, then whole eggs with 30 g starch alternately. Stir in rum. Sieve 50 g starch, flour and baking powder. Stir into the butter-egg-cream in 2 portions. Beat the egg white with 1 pinch of salt until stiff. Fold into the dough in 2-3 portions.
Preheat the oven grill. Grease a box cake tin (25 cm long; approx. 1.5 l capacity) and line the bottom with a strip of baking paper. Spread a thin layer (approx. 2 tbsp. dough) on the baking paper. Place the box cake tin on the grill rack and grill on the second rack from below under the hot grill for about 3 minutes until the dough is light brown. Take out immediately and spread the next thin layer of dough on the baked one. Now only grill for about 2 minutes.
Spread 4 plums on the 2nd layer of dough and spread the next thin layer (2-2 1⁄2 tbsp. dough) over it. Grill for about 2 minutes. Then grill another 1-2 layers of dough without plums. Then again 1 layer with plums (see sketch on the right) and grill with 1 more layer of dough. Continue in this alternation until the whole dough is used up. Bake the last 2 layers without plums and only grill the last layer light brown (!). Then switch the oven (electric oven: 180 °C/circulating air: 160 °C/gas: see manufacturer). Bake the cake for approx. 10 minutes (stick test).
Place the finished Baumkuchen in the mould on a cake rack and let it cool for about 15 minutes. Remove from the edge with a knife, turn over onto a plate, remove the paper and let it cool down.
Whip the cream until stiff, adding 1 vanilla sugar and 1⁄4 tsp cinnamon. Cut open the Baumkuchen. Serve with cream and cinnamon.