Add the sugar and stir. Finally add the salt and the softened butter at room temperature. The dough should be soft.
Put the dough in a pastry bag, then fill the buttered molds with the mixture up to about 1 cm from the edge. Let the babà rise for about two hours in the oven off, with the light on.
The dough must come out of the molds, forming a small dome.
Cook the babà at 180 ° in a preheated ventilated oven for about 13/15 minutes. Remove from the molds and leave to cool.
Now prepare the rum baguette: in a saucepan heat water, sugar and lemon zest. Bring to a boil and cook for about ten minutes. Then, after the syrup has cooled, add the rum and stir.
Transfer the rum to a bowl and then immerse the babà completely until it is soaked in the sauce.
Brush the babà with the apricot jam now to make them shiny. Let it rest in the fridge for about 1 hour.
If you prefer, cut the rum babas in half and stuff them with whipped cream and fresh fruit, otherwise, enjoy them at nature.