Preheat the oven to 200°C.
Sprinkle orange zest, juice, and two tablespoons of sugar over rhubarb in a roasting tin.
Bake rhubarb for ten minutes until tender and set aside to cool.
Whisk remaining caster sugar, yeast, and warm milk in a bowl until dissolved.
Beat eggs, butter, and flour into the yeast mixture until the batter is smooth.
Fold half of the chopped roasted rhubarb into the batter.
Divide mixture into six greased moulds and let rest for 30 minutes until doubled in size.
Bake the babas for 15 minutes until golden and cool before removing from moulds.
Boil brown sugar and water for two minutes, then stir in rum to create a syrup.
Soak the cooled babas in the rum syrup.
Whisk double cream to soft peaks and fold in the remaining chopped rhubarb.
Serve babas topped with rhubarb cream and reserved roasted rhubarb pieces.