In a mixing bowl, combine your unfed sourdough starter with flour, room-temperature water, and light brown sugar. Stir until well blended, then cover with a damp cloth. Let this mixture ferment at room temperature for 6-8 hours.

Using a stand mixer, combine all-purpose flour, cornstarch, the fermented sweet starter, large eggs, whole milk, salt, and granulated sugar. Mix on low until a rough dough forms. Gradually add softened butter, mixing until smooth and elastic.

Transfer the dough into a lightly oiled bowl, cover, and let it rise at room temperature for 4-6 hours, or refrigerate overnight.

In a small saucepan over low heat, warm the heavy cream until just simmering. Pour it over dark chocolate pieces, stirring until melted. Mix in cocoa powder, granulated sugar, softened butter, vanilla extract, and walnuts if using.

On a floured surface, roll the risen dough into a rectangle. Spread the cooled chocolate filling over it, roll tightly into a log, slice lengthwise, and twist halves into a spiral before placing in a greased loaf pan.

Cover the shaped dough and proof for 2-4 hours until it has expanded.

Preheat your oven to 350°F (175°C). Bake the babka for 35-40 minutes until golden brown.

While baking, prepare the glaze by heating granulated sugar and water until the sugar dissolves. Brush the syrup over the warm loaf after baking.

Allow the babka to cool in the pan for 10-15 minutes before transferring it to a wire rack.