Make the cream about 12 hours before you want to serve it. Lightly whip the double cream, then fold in the yogurt. Put this in a bowl and sprinkle evenly with the sugar. Cover with cling film and put in the fridge. The sugar will become soft and treacly.
Preheat the oven to 180°C fan (375°F), Gas Mark 5.Put the plums into a roasting tin or a big ovenproof dish or gratin dish in which they can lie in a single layer (snugly; you don’t want the juices around them to reduce and burn). Arrange the fruits so they are cut sides up.
Scatter the stem ginger around the plums. Mix the sugar with the ground ginger and sprinkle it over the top. Squeeze the lime juice over and tuck the pieces of lime zest under the fruits, then pour the 150ml (5fl oz) rum around them.
Bake for 15–30 minutes (how long it takes depends on the ripeness of the plums). The fruit should be tender when pierced with a sharp knife, but not collapsing.
Leave to cool completely; the juices should thicken as they cool. If they aren’t thick enough, drain off the juices and boil them in a saucepan until they become more syrupy. Add the remaining 3 tablespooons of rum.
Serve the plums, at room temperature, with the muscovado cream.