Grease a rectangular springform pan (approx. 24 x 35 cm; alternatively a high casserole dish) and sprinkle with breadcrumbs. Peel, quarter and core the apples. Sprinkle with lemon juice immediately. Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: level 2).
Cream butter and sugar with the whisks of the mixer for 3-4 minutes. Stir in the eggs one by one. Mix flour and baking powder and sieve over them. Stir in cream and rum briefly. Spread half the dough into the form.
Cover with apples and spread the rest of the dough on top. Sprinkle with brown sugar. Bake in a hot oven for about 20 minutes.
Turn down the oven temperature (electric oven: 150 °C/circulating air: 125 °C/gas: level 1-2), continue baking for approx. 40 minutes. Leave to cool down. Then dust the apple cake with icing sugar. Whipped cream is delicious with it.