First, grease a 12-inch springform pan with the melted butter, then flour it. Prepare apples by peeling and coring, then cut them into quarters and slice.
Whisk eggs and sugar in a bowl until creamy. Add the flour and baking powder, then combine. Add milk, butter and vanilla and then mix. Add the apples and cranberries to the batter. Pour into the greased and floured pan, and put pan on a cookie sheet.
Bake on bottom shelf of oven at 375°F (190°C) for 10 minutes. Move to top shelf and bake at 375°F (190°C) for 50 minutes, checking with wooden skewer for doneness. Reduce heat if cake gets too dark – it should look golden and caramelized. When baked, remove from oven and carefully pull knife along the ring but do not open the springform. Let cool in fridge very well before removing springform. If you store the torte for longer than a day, you should transfer it to a glass plate; otherwise, the cake might oxidize on metal.
When ready to serve the torte, prepare the sauce. Melt butter with sugar until it lightly caramelizes. Add cream and vanilla and bring to simmer until well blended. Add rum to taste.