In a saucepan, whisk together 2 tablespoons of bread flour and ⅓ cup of water over medium heat. Stir continuously for 3–4 minutes until the mixture thickens into a smooth paste.

In a mixer bowl, combine 2 cups of bread flour, ¼ cup of sugar, ½ teaspoon of salt, and 1 ½ teaspoons of active dry yeast. Add in ⅓ cup of whole milk, 1 large egg, and the cooled tangzhong. Mix on low speed for about 5 minutes.

Lightly oil a container and transfer the dough into it, ensuring it's well covered. Place the container in the refrigerator and let the dough ferment overnight for 8–12 hours.

Melt 2.3 oz of dark chocolate and 4 tablespoons of softened butter in a heatproof bowl until smooth. Stir in 3 tablespoons of powdered sugar, 2 tablespoons of cocoa powder, and a pinch of sea salt.

Dust your work surface with flour and roll the cold dough into a rectangle measuring approximately 12x15 inches. Spread the chocolate filling across the dough and sprinkle with chopped pistachios.

Transfer the braided dough into a greased loaf pan, cover with a clean kitchen towel, and let it proof for 60–90 minutes.

Preheat your oven to 350°F (180°C). Bake the proofed dough for 30–35 minutes until golden brown.

Prepare a simple syrup by simmering 3 tablespoons of water and 2 tablespoons of sugar until dissolved. Brush this syrup over the warm loaf.

Allow the babka to cool in the pan for about 20 minutes before transferring it to a wire rack.