Step 1 Make the dough: In a large bowl, whisk together the melted butter, warm water, sugar, salt, and yeast. Add the eggs and egg yolk and whisk until evenly combined. Add the flour all at once, and stir with a wooden spoon until uniform and all of the flour is absorbed. The dough will be wet, lumpy and somewhat elastic (it will firm up in the fridge and smooth out when you knead it later). Cover loosely with plastic wrap (be sure the bowl is completely covered but don't make it airtight) and let sit at room temperature for 2 hours, then refrigerate for at least 3 hours or up to three days.
Step 2 On the day of baking, grease a 9x5-inch loaf pan generously with butter. Dust a clean work surface with flour. Remove the dough from the refrigerator, transfer it to the work surface, and dust it lightly with flour. Knead with your hands, sprinkling more flour as necessary so the dough doesn't stick, for 30 seconds. Roll out the dough into a 14-inch square, dusting more flour underneath and over the dough as necessary; it should be about ⅛ inch thick.
Step 3 Using an offset spatula, spread the Nutella over the dough, leaving a ½-inch border. Sprinkle the chocolate over the Nutella. Starting with the side closest to you, roll the dough tightly into a log; turn it vertically, so one end of the log is facing you, and place seam side down. Using a sharp serrated bread knife, cut the log in half lengthwise. Turn the cut sides up and twist the strands together, keeping the cut sides facing up. Transfer the twisted dough to the prepared loaf pan, tucking the ends under if necessary. Cover the babka loosely with plastic wrap (not airtight) and let sit at room temperature for 90 minutes. It will rise just a bit.
Step 4 Towards the end of the rising time, preheat the oven to 350°F and set an oven rack in the middle position.
Step 5 Bake for 45 to 50 minutes, until the babka is a rich golden brown color. A toothpick or cake tester inserted into the center of the loaf should come out without any wet dough sticking to it (melted chocolate is okay). If you have an instant-read thermometer, it should read between 190°F to 200°F in the center of the loaf.
Step 6 Meanwhile, make the syrup: In a small saucepan, combine the water, sugar, and salt. Bring to a boil over high heat, stirring until the sugar dissolves. Remove from the heat and set aside.
Step 7 Place the pan with the baked babka on a rack. Immediately brush or drizzle the syrup over top. Let cool in the pan for 15 minutes, then turn out and cool completely before slicing.
