Boil the sugar and apple juice in a wide-bottomed pan without stirring. Reduce the heat and simmer, shaking the pan occasionally, until a golden brown caramel has formed. Stir in the butter and salt, simmer for approx. 5 mins. Allow to cool, then stir in the rum.
Cut the pineapple lengthwise into eighths, remove the stalk, place on a baking tray lined with baking paper.
Coat the pineapple with the caramel, place under a grill preheated to 250 °C for approx. 10 mins., brushing with the caramel at regular intervals.
Tear the panettone into large pieces, place on a baking tray.
Dry for approx. 30 mins. in the centre of an oven preheated to 120°C. Bring the pineapple juice and sugar to the boil in a small pan while stirring, allow to cool a little, then stir in the rum. Soak the panettone with the liquid.
Serve: arrange the pineapple on plates, serve with one scoop of ice cream and the panettone, garnish with Thai basil and the remaining caramel.