1) In a large mixing bowl, stir together the water, sugar, two cups of the flour, yeast, salt and butter. Mix until fairly evenly blended.
2) 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 smooth and springy.
3) Place it 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.)
4) After an hour (or the end of the cycle), turn out the dough onto a lightly floured surface, flatten it gently and fold it in thirds, like a letter. Place the dough in a lightly greased plastic bag that has enough room for the dough to expand, and refrigerate for at least 2 hours, until thoroughly chilled. (For best flavor, refrigerate it overnight.)
While the dough is chilling, prepare the 2 sticks of butter for rolling into the dough. Cut each stick in half lengthwise and place all four 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 6 x 9 inches. Wrap the butter well and put it back in the refrigerator.
1) Remove the dough from the refrigerator, place it on a lightly floured surface and roll it out until it's about 10 x 20 inches. Remove the butter from the refrigerator and place it in the center of the dough.
2) Fold the upper third of the dough over the butter and the lower third over the upper third (like a letter). Pinch the edges together so the butter is completely enclosed. Roll the dough out again until it's about 10 x 24 inches. This time fold the two ends so they meet in the middle and then fold that in half like a book.
3) Wrap the dough in lightly floured plastic wrap and refrigerate it again for at least 2 hours (or, you can leave the dough in the refrigerator for several days, until you're ready to use it).
4) To finish your Pain au Chocolat, remove the dough from the refrigerator, cut it in half and return one half to the refrigerator.
5) Roll the other half out until it's about 9 x 25 inches. Trim each edge to make it 8 x 24 inches. With a bench knife, cut the dough into eight 4 x 6 inch pieces.
6) Place 1 (or 2) 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. Cover and let rise in a warm place until they are light and puffy looking. Repeat with the remaining dough.
7) Just before baking, brush the egg/salt glaze over the tops of the Pain au Chocolat. Bake in a preheated 425°F oven for 18 to 20 minutes, until golden brown. Remove from the oven and allow them to cool a bit before you bite into them; the structure needs a chance to set.