Heat a saucepan over medium heat and add butter and cream. Wait until the butter has melted and the mixture is steaming. Then add the chocolate and stir until melted, then remove from the heat. Whisk in the powdered sugar and cocoa powder. Transfer to a bowl and let cool until thickened to a spreadable consistency, about 1 hour.

In a loaf pan, grease it with butter and line it with parchment paper. Then, on a floured surface, roll the chilled dough into a rectangle. Spread the filling on the dough to the edge on three sides, leaving a border on one short side. Starting at the short side opposite the border, roll the dough into a tight coil and pinch the seam to seal.

Using a sharp knife, cut the dough in half lengthwise. Position each half parallel to the other with the cut side facing up. Twist the halves together, keeping the cut sides facing up, and tuck the ends under. Now gently place it in the prepared loaf pan. Then cover the loaf pan with cling wrap and let it rise in a warm place until noticeably puffed.

Preheat the oven to 350°F and bake the risen loaf for 40 minutes or until the top is golden brown. You can test it by inserting a wooden toothpick into the centre; if it comes out clean, it is ready.

While the babka bakes in the oven, combine the water and sugar in a small saucepan. Bring it to a simmer over medium heat, stirring until the sugar is fully dissolved. Then remove it from the heat. Now brush the warm loaf with this syrup as soon as it comes out of the oven. Let the chocolate babka cool down at room temperature for 30 minutes. Then it is ready to be served.