Peel the pears, remove the tops, and reserve the caps with stems.
Finely chop the apricots and almonds, then place them in a bowl with the rum. Let macerate for 1 hour.
Hollow out the pear cores generously and fill the cavities with the apricot-almond mixture.
Arrange the pears in a baking dish. Drizzle each with the maceration syrup, top with a knob of butter, sprinkle with caster sugar, and add 2 tablespoons of water around them. Preheat oven to 150°C (thermostat 4). Bake for about 40 minutes.
Monitor closely—the pears should be tender but not mushy.
Remove from the oven and baste each pear with the cooking juices.
Serve warm, optionally with whipped cream or apricot coulis.
