1. Peel the apples neatly using a small paring knife, and scoop out the cores with an apple corer. Pat dry with kitchen paper, then brush all over with softened butter. Roll in the demerara sugar to coat.
2. Preheat the oven to 190C/375F/gas mark 5. Place the apples in a roasting tin or baking dish and roast in the oven for 10 minutes.
3. Pour in the apple juice and scatter over the crushed peppercorns and vanilla pod. Spoon the juice over the apples, then return to the oven. Roast, uncovered, for a further 20 minutes, basting the fruits every 5 minutes or so. On the final basting, trickle over the Armagnac, if using.
4. Allow to cool for 10 minutes or longer, basting the apples occasionally with the pan juices.
5. To serve, lift the apples into a serving dish and strain the pan juices over. For a simple dessert, serve warm with pouring cream or crème anglaise and cumin or hazelnut shortbread.