II
The Method
1
Butter the cylindrical or barrel-shaped baba moulds generously. Dust with plain flour and knock out the excess. Do not use sugar — sugar on the mould surface caramelises, closes the crust's pores, and permanently reduces absorption.
2
Combine flour, yeast, salt, and sugar in the bowl of a stand mixer fitted with a dough hook. Add the eggs and mix on a low speed until a cohesive dough forms. Increase to medium speed and work until the dough is smooth and pulls away from the bowl's sides. The dough should be soft and slightly tacky — not stiff. A tight, over-enriched crumb resists absorption; the dough must remain open enough to welcome the syrup.
3
With the machine running on medium-low, add the softened butter piece by piece, waiting until each addition is fully incorporated before adding the next. Continue mixing until the dough is glossy, elastic, and again clears the bowl sides. It will be softer than a bread dough.
4
Cover the bowl and leave the dough to prove at room temperature until roughly doubled in volume.
5
Knock back the dough and divide it between the prepared moulds, filling each no more than half full to allow for oven spring. Prove again until the dough crowns just above the rim of the mould.
6
Bake in a preheated oven until the babas are a deep golden brown and a skewer inserted at the centre comes out clean. Turn out immediately and transfer to a wire rack. The babas must be baked completely dry — an underbaked baba will collapse in the syrup and lose all structure. Allow to cool fully to room temperature; cold reduces porosity, but a fully cooled dry baba absorbs more efficiently than a warm one.
7
Combine the water and sugar in a saucepan over a medium heat, stirring until the sugar has fully dissolved. Remove from the heat and allow to cool to 40–45°C. Stir in the dark agricole rum. The syrup quality is permanent and uncorrectable at service — the rum used here defines the finished baba entirely. This is where the dish lives or dies: the syrup must be held at 40–45°C throughout soaking — hot enough to penetrate the crumb but not so hot that it dissolves and closes the crust's surface.
8
Place the dry, room-temperature babas one at a time into the warm syrup. Each baba will sink immediately upon immersion. Monitor without intervention. As absorption progresses the baba will rise. When it floats steadily at the surface it has reached maximum absorption. Remove it at once.
9
Apply the squeeze test: hold a soaked baba gently between two fingers and apply light pressure. Syrup should yield under that pressure. Release. No syrup should remain weeping from the surface spontaneously. Cut a baba and examine the cross-section — the colour must be a uniform amber from edge to centre. Any pale or white area at the centre indicates under-soaking; return the baba briefly to the syrup.
10
Serve the soaked babas at room temperature alongside softly whipped chantilly.