To make the dough: In a large mixing bowl, stir together the water, sugar, 2 cups of the flour, yeast, salt, and butter. Mix until fairly evenly blended., Add the remaining flour and stir until the dough pulls away from the side of the bowl. Turn the dough out and knead it until it just starts to smooth out. You don't want to over-knead it at this point, since it's going to spend a considerable amount of time rising., Place the dough in a lightly greased bowl, cover, and let rise for about an hour, until puffy. (The dough can be prepared to this point in a bread machine with at least a 1 1/2 pound capacity. Simply place all of the ingredients in the bucket, select dough or manual, and press start.), After an hour at room temperature, refrigerate the dough (in its covered bowl) for 8 to 16 hours; overnight is your best bet., To prepare the butter: Just before the dough is ready to come out of the fridge, prepare the butter for rolling into the dough. Cut each of the three sticks in half lengthwise and place all six pieces on a floured piece of waxed paper or plastic wrap. Sprinkle flour on the top surface of the butter, cover with another piece of paper or plastic and gently pound it with a rolling pin until it becomes malleable. Then roll the butter out until it's about 8" x 8"., To assemble the rolls: Remove the dough from the refrigerator, place it on a lightly floured surface and roll it into a 12" square. Place the butter in the center of the dough at a 45° angle; it'll look like a diamond inside the square. Fold the four flaps of dough into the center to enclose the butter, pinching them together as best you can., Roll the dough into a 10" x 20" rectangle. Fold one third into the center, then the opposite third over the first, like you were folding a business letter; this is called a letter fold. Turn the dough 90°, roll it into a 10" x 20" rectangle again, and do another letter fold., Wrap the dough in lightly floured plastic wrap and refrigerate it again for an hour. Remove the dough from the fridge, and give it two more letter folds: rolling, folding, turning 90°, rolling, and folding. Wrap the dough in lightly floured plastic wrap and refrigerate it again for at least 8 hours (or up to 24 hours, until you're ready to use it)., To finish your pain au chocolat: Remove the dough from the refrigerator, cut it in half and return one half to the refrigerator., Roll the other half out until it's a generous 8" x 24". With a bench knife, cut the dough into eight 4" x 6" pieces., Place one or two pieces of chocolate at one end of each piece and roll it up into a tube. Place, seam side down, on a lightly greased or parchment lined baking sheet. Press down on the tops of the rolls to flatten them into a rectangle shape. Repeat with the remaining dough. Cover and let rise in a warm place until they're light and puffy looking, about an hour., Towards the end of the rising time, preheat the oven to 425°F., Just before baking, brush the egg/salt glaze over the tops of the rolls. Bake the rolls for 18 to 20 minutes, until golden brown. Remove them from the oven and allow them to cool a bit before you bite into them; the structure needs a chance to set., Store any leftover rolls, well wrapped, at room temperature for several days; freeze for longer storage.