In the bowl of a stand mixer, whisk together the bread flour, sugar, instant yeast, and salt. Add the warm milk and eggs. Using the dough hook attachment, mix on low speed for approximately 5 minutes, or until the mixture forms a rough dough.

Increase the mixer speed to medium and knead the dough for 5 additional minutes, or until it begins to pull away from the sides of the bowl. Allow the dough to rest for 10 minutes. Resume mixing on medium speed and add the softened butter, one tablespoon at a time, incorporating each portion before adding the next. Continue kneading for 5–8 minutes, or until all butter is fully incorporated. Knead for an additional 10 minutes, until the dough forms a smooth, elastic ball and no longer clings to the sides of the bowl.

Transfer the dough to a lightly greased bowl. Cover with plastic wrap or a fitted lid and allow it to rise at room temperature for 1½ hours. Then refrigerate the dough for at least 1 hour or up to 2 days.

In a small saucepan over low heat, melt the chopped chocolate, butter, sugar, and cocoa powder. Stir continuously until smooth. The texture may appear grainy due to the sugar, but this will resolve during baking.

Divide the chilled dough into two equal portions. On a lightly floured surface, roll one portion into a 10×15-inch rectangle. Spread half of the chocolate filling evenly over the dough, leaving a ½-inch border at the top. Roll the dough tightly from the short end into a log. Wrap in plastic wrap and freeze for 10 minutes. Repeat with the second portion of dough.

Grease two 9×5-inch loaf pans and line them with parchment paper, allowing excess to hang over the edges. Remove one log from the freezer and slice it lengthwise. Twist the two halves together with the cut sides facing outward. Place the braided dough into the prepared loaf pan. Repeat with the second log.

Cover both pans with plastic wrap and allow the dough to rise at room temperature for 1½ to 2 hours, or until it reaches nearly the top of the pans.

Preheat the oven to 350°F (175°C). Bake the loaves for approximately 35 minutes, or until the tops are golden and a skewer inserted into the center emerges clean or with a small amount of melted chocolate.

While the loaves bake, combine the water and sugar in a saucepan over medium heat. Simmer until the sugar is completely dissolved, then remove from heat. While the baked loaves are still warm, brush them generously with the syrup, dividing it evenly between both.

Allow the loaves to cool in their pans for 10 minutes. Lift them out using the parchment overhang and transfer to a wire rack to cool completely before slicing and serving.