Mix together 30g starter with 60g flour and 30g water. Knead it for a minute or two into a stiff dough ball.

Place this into a lightly oiled jar. Brush the top of the ball dough with a little water (so it doesn't dry out too much overnight). Loosely cover with a lid and leave it to rise for 8-12 hours until more than doubled.

Add the flour, sugar, salt, eggs, milk, and starter to the bowl of a stand mixer fitted with a dough hook. Turn the mixer on low and combine until it forms a thick but slightly sticky dough. Mix this dough for around 5 minutes to begin developing the gluten. 

Add the cubed butter, a few pieces at a time. Incorporate each cube before the next addition.

Turn the mixer on medium and keep it mixing for around 10-15 minutes until the sticky dough strengthens, comes together, and pulls away cleanly from the sides of the bowl. If the mixer gets too hot, turn it off for 5 minutes and leave the dough to sit. It responds very well to rest.

Once finished mixing, leave the dough to rest for a few minutes, then grab a piece and see if you can stretch it out thin so it’s almost see-through, without it tearing. This is called the 'window pane' effect and shows proper gluten development. 

Once risen, cover the bowl with plastic wrap or an airtight lid and place it in the fridge overnight.

Prepare the chocolate filling so it has time to cool. In a saucepan over low heat, melt chocolate and butter together. Once melted, remove it from the heat, and while it’s still warm, stir in powdered sugar and vanilla. Pour into a bowl and let it cool until it becomes a spreadable paste.

Grease and line two 9x5 inch loaf pans with parchment paper.

Pull the proofed dough from the bowl and tip it onto a lightly floured bench. Cut it into two even pieces.

Roll one piece into a rectangle measuring around 11x14 inches (27x35 cm).

Spread over ½ the cooled chocolate filling, leaving an ½ inch (1cm) border around all the sides. Roll it up lengthwise into a log and place it in the fridge for 10-15 minutes. This cools down the chocolate and makes it easier to cut later.

Repeat with the other dough piece.

Once chilled, it's time to shape and braid the sourdough babka. Slice a log in half lengthwise. Cut it with a knife; don't push down on the dough, or it will squash. Fold the two ends over, lift the left half over the right half, then the right over the left, and repeat down, leaving the chocolate exposed. Place the braid into a prepared loaf pan. You will likely need to compact it a bit to make it fit.

Leave the babkas to rise in a warm and humid spot until they double in size. The chocolate filling will crack apart as it rises, which is normal.

Preheat the oven to 350°F/180°C and place a rack in the middle of the oven.

Once the babkas have risen, bake them for around 40 minutes until deep brown. If browning too much, cover the tops loosely with foil.

While baking the babkas, prepare the sugar syrup to glaze them.

Combine the sugar and water in a small saucepan over medium heat. Bring it to a simmer until the sugar has dissolved, then remove it from the heat.

Once the babkas are removed from the oven, brush them liberally with the syrup.