Preheat oven to 160°C. Grease a 3L-capacity ovenproof dish with the extra butter and set aside.
Place ¼ cup (60ml) rum in a small saucepan over low heat and bring to a simmer. Place raisins in a heatproof bowl and pour over the rum. Set aside to soak and cool slightly.
Place the milk, cream, vanilla seeds and pod, cinnamon and remaining ¼ cup (60ml) rum in a medium saucepan over medium heat, and bring to just below a simmer. Discard the vanilla pod.
Place eggs, yolks and sugar in a large bowl and, using a whisk, gently stir to combine (try not to incorporate too much air). Pour over the hot milk mixture, whisking constantly until combined.
Butter both sides of the brioche and place in the prepared dish, layering each slice so that they overlap. Scatter over the raisins and any soaking liquid, then pour over the egg mixture, making sure all the brioche is covered. Set aside for 15 minutes to soak.
Cover dish with foil and bake for 30 minutes. Remove foil and sprinkle with extra demerara sugar, then cook for a further 7-8 minutes until custard is just set, but still a little wobbly. Stand for 15 minutes. Serve warm with ice cream.
