Activate sweet stiff starter: The night before, mix the sourdough starter, all-purpose flour, water and brown sugar in a container. Cover and set in a warm place overnight, or at least 8 hours. 

Make the dough: Combine all-purpose flour, cornstarch, sweet stiff starter, milk, eggs and sugar in a large bowl and stir until all the flour is hydrated. Knead the butter into the dough one tablespoon at a time. Continue kneading until the butter has been absorbed and the dough no longer feels greasy. Cover the bowl with plastic wrap and let it rest for 1 hour. 

Strengthen the dough: Coat a clean work surface with a light layer of oil. Turn your dough out onto your work surface. Gently knead the dough with the base of your palms about 5 to 10 times, or until the dough feels smooth and elastic. You don’t want to build too much strength in your dough or your babka will end up too tough. 

First rise: Gather your dough into a tight ball and place it inside a clean lightly-oiled bowl. Cover the bowl with plastic wrap and let it rise until doubled in volume, about 6 to 8 hours (this could be longer, pay attention to the increase in volume). 

Cold proof: Deflate the dough and gather it into a tight ball. Cover with plastic wrap and place the dough into the refrigerator for an overnight rest. 

Make the filling: Combine the chocolate, sugar, cocoa powder and butter in a small mixing bowl. Set aside. Heat the cream up in a small saucepan over medium heat until it begins to simmer (don't let it boil over), about 5 minutes. Pour the cream over the chocolate mixture and let it sit for 2 minutes or until the chocolate and butter begins to soften. Stir the mixture with a rubber spatula or wooden spoon until all the ingredients are fully combined. Set aside and let the mixture cool completely.

Fill the dough: Turn the dough out onto a lightly floured work surface. Using a rolling pin, flatten the dough out into a 10 by 14 inch rectangle (it doesn’t have to be exact). Spread all of your chocolate filling over the dough, sprinkle an even layer of walnuts over the chocolate (if using). 

Shape your babka: Starting with the longer side of the rectangle, roll the dough into a tight cylinder. Using a sharp knife, slice the dough lengthwise into two equal portions. Twist the two portions of dough together. Gently place the dough into a loaf pan lined with parchment paper. 

Final rise: Cover the loaf pan with plastic wrap and let it rise until it appears puffy and has doubled in volume, about 3 to 4 hours. 

Bake: Once your dough is almost ready, preheat your oven to 350 F. Bake your loaf for 35 to 40 minutes or until it has browned and the internal temperature registers at 180 to 200 F when probed with an instant read thermometer. 

Make the syrup: Combine water and sugar in a small saucepan set over medium heat. Swirl and heat until the sugar has fully dissolved, about 3 to 5 minutes.   

Finish loaf: While your loaf is still warm, poke holes all while inside the loaf pan using a bamboo skewer or a small knife. Pour the simple syrup all over the loaf. Let the syrup soak for 10 minutes. Transfer the loaf to a cooling rack and let it cool for at least 30 minutes. 

Serve and store: Serve the babka while still warm or at room temperature. Store leftover slices in an airtight container at room temperature for up to 5 days. 

Instructions for freezing: Wrap slices in foil and freeze for up to a month. Let the slices defrost at room temperature before serving.