In a stand mixer bowl, combine bread flour, slightly warm milk, eggs, sugar, and starter until shaggy. Rest 20–30 minutes.
Add salt. Knead with the dough hook.
Add butter gradually (a few pieces at a time) until fully incorporated
Continue mixing 8–10 minutes until dough is soft, elastic, and slightly tacky
Cover and let rise 2½–3 hours at room temperature until puffy
Refrigerate overnight
Filling
Gently melt chocolate and butter together (microwave in short bursts or bain-marie)
Whisk in cocoa powder, then powdered sugar (add espresso or vanilla if using). Use while warm, glossy, and spreadable (Nutella-like)
Roll chilled dough to a 25×35 cm (10×14 in) rectangle
Spread filling evenly, leaving a 1 cm border clean
Roll into a tight log, seam side down
Slice the log lengthwise to expose layers
Twist the two strands together with cut sides up. If the braid is longer than the pan, fold gently to fit
Place the braid in a parchment-lined 9×5 in loaf pan
Cover and proof 2–2½ hours until pillowy and ~30–40% bigger (a finger dent springs back slowly)
Preheat oven to 350°F
Brush top with egg wash. Bake 35–40 minutes; tent with foil if browning early
Optional doneness check: internal temp 200–210°F at the center
Glaze
Simmer sugar and water until dissolved
Brush syrup generously over the hot babka immediately after baking. Cool in pan 15 minutes, then transfer to a rack to cool before slicing
Enjoy!
Notes
Same-day option: bulk 3–4 hours at room temp, chill 1 hour to firm for shaping, then roll, braid, proof, and bake (slightly less flavor depth than an overnight chill).
If filling thickens while shaping, warm briefly and stir smooth; aim for warm-spreadable, not runny.
Freezing: freeze the braided (unproofed) loaf, wrapped well; thaw overnight, proof, and bake. Or freeze baked loaf (cool completely, wrap well) up to 2 months; rewarm slices.