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1
Combine flour, yeast, sugar, and salt in a bowl. Add the beaten eggs and lukewarm milk. Work the mixture vigorously — beat or stretch it against the bowl — until it forms a loose, elastic batter rather than a firm dough. For baba, fold in the drained currants. The dough is ready when it is cohesive, very slack, and pulls away from the sides of the bowl cleanly.
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2
Transfer the batter to greased individual baba moulds or a savarin ring, filling each no more than half full to allow for rise. Cover and leave at room temperature until the dough has risen to the rim of the mould and looks open-structured and airy.
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3
Bake in a preheated oven until the pastry is completely dry throughout and beginning to colour on the surface. Tap the base of an unmoulded baba: it must sound hollow — a dull thud indicates moisture remains and the structure will collapse under soaking. This dryness is intentional.
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4
Dissolve the sugar in the water over moderate heat, bring to a brief simmer, then remove from the heat. Add the rum, kirsch, or citrus. Keep the syrup warm — hot enough to penetrate readily, not so hot as to damage the structure.
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5
This is where the dish lives or dies. While the baked baba is still warm, submerge it in the warm syrup. Turn it, and press gently but repeatedly to encourage absorption. Continue until the finished pastry is approximately 60 percent syrup by weight. Apply the squeeze test: press the baba gently — it should yield like a saturated sponge, and syrup should bead at the surface. If it resists and feels springy, it is under-saturated; return it to the syrup. If it collapses and falls apart, it has been over-soaked.
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6
Lift the saturated baba from the syrup and set it on a rack. Allow it to rest for one hour before serving. During this time the syrup distributes evenly throughout the interior. The surface should appear glossy and uniformly moist with no dry patches visible.