In a stand mixer bowl, add the dry ingredients: flour, sugar, yeast. Mix well with a spoon or a whisk.
Add the butter (cut into cubes), the eggs, and the milk. Attach the dough hook to the stand mixer and mix on low to medium speed until the dough forms into a ball. Add the salt and mix for another 5-8 minutes on medium-high speed or until the dough is smooth and has pulled away from the sides of the bowl.
Cover the bowl with plastic wrap and let the dough rise in a warm place for 1-2 hours or until doubled in size.
Meanwhile make the chocolate filling: into a medium-sized bowl, add the dark chocolate, butter, powder sugar, and cocoa powder.
Place the bowl in the microwave for 1-2 minutes or until the chocolate and the butter are melted. Mix with a spoon until the mixture is smooth and creamy.
Transfer the dough onto a clean lightly floured surface and cut it in half. (this recipe makes 2 chocolate babka) Roll the dough with a rolling pin into a rectangle shape.
Take half of the chocolate filling mixture and spread an even layer on the dough. Gently roll out the dough just like you would do with a cinnamon roll.
Place the dough roll into the freezer for 15 minutes. (optional, but makes it so much easier to cut the dough.)
With a sharp knife, cut the dough roll lengthwise into half. With the cut side facing up, starting at the top, pinch both ends together. Gently braid the dough placing the right side over the left side, repeating this process until a braid forms.
Prep a baking loaf pan with parchment paper, then gently place the dough braid into the loaf pan and cover with a towel, letting the dough rise for the last time for 30-50 minutes in a warm place or until doubled in size. Bake in a 180c (350f) preheated oven for 30 minutes or until the top is golden brown.
Make the sugar syrup: add the sugar and water to a small saucepan and cook on medium heat and bring the sugar and water to a boil. When the sugar syrup dissolves completely, remove the pan from the heat and let it cool completely.
Take the chocolate babka loaf out of the oven and brush immediately with the sugar syrup. Let the chocolate babka cool for 10-15 minutes, slice, and serve warm!