Grease a deep 12-hole muffin tin or metal baba moulds.
Boil currants with rum and water in a pan, then cool.
Sift flour, yeast, and salt into a large bowl.
Whisk eggs, milk, and honey, then beat into flour with 115g butter until glossy.
Drain currants, reserving the rum, and stir fruit into the batter.
Spoon mixture into tin and let rise for one hour in a warm place.
Bake at 190°C for 12-15 minutes until golden brown.
Dissolve sugar in water over heat, then add reserved and additional rum and honey.
Cool babas for five minutes before turning them into a shallow dish.
Pour half of the syrup over the babas and rest for five minutes.
Turn babas over, pour remaining syrup, and rest for ten minutes.
Chill in the fridge for at least two hours before serving with cream.