Add the cranberries, lemon peel, orange peel, and rum to a bowl and let the fruit soak in the alcohol. Combine the flour, baking powder, sugar, cinnamon, ground cardamom in a large bowl. Add the egg, cream cheese, and softened butter to the dry ingredients and knead the mixture into a smooth dough. Then knead the almonds and soaked cranberries into the dough. Roll the dough out on a floured work surface to about 1-inch thickness and then cut the dough into 10 equal 1 x 1-inch pieces. Place the dough squares on a baking tray lined with parchment paper, transfer the baking tray to a preheated oven, and cook at 400°F for about 20 minutes. Brush melted butter over the cooled cranberry orange scones and sprinkle powdered sugar on top.
Whisk the cream cheese, sugar, cinnamon, and vanilla extract until combined. Completely dissolve the gelatin sheets in hot water and then stir the gelatin mixture into the cinnamon cream cheese mixture. Fold the whipped cream into the cinnamon cream cheese mixture and refrigerate the cinnamon mousse for 2 hours.
Arrange the cranberry orange scones in 2 circles inside a 12-inch springform pan. Pour the cinnamon mousse over the scones, smooth out the top, and refrigerate for 2 hours.
Soak the gelatin sheets in cold water. Add the plums, red wine, sugar, and cinnamon stick to a saucepan over medium heat and cook until the plums start to disintegrate. Squeeze the water out of the soaked gelatin sheets and add them to the saucepan. Remove the cinnamon stick from the saucepan, add the basil leaves, and mix well. Remove the saucepan from the heat and let cool. Pour the spiced plum sauce over the cinnamon mousse in the springform pan and refrigerate for 1 hour.
Beat the egg whites and salt with a hand mixer on high before gradually mixing in the powdered sugar and a few drops of lemon juice. Spoon the mixture into a piping bag with a star tip and pipe 8 portions onto a baking tray lined with parchment paper. Transfer the baking tray to a preheated oven and cook at 200°F for 1-1½ hours with the oven door open. Let the meringue cookies cool after removing them from the oven and then crumble them over the cranberry orange scone cake before serving.