Mix all dough ingredients to form a soft dough. Cover bowl tightly with plastic wrap and refrigerate for one hour. Meanwhile, make the butter square. Unwrap three sticks of butter and cut each one into eighths. Sprinkle the flour over top and begin kneading these together to form one relatively smooth ball. Lay out a piece of plastic wrap, plop the butter-flour ball on top, and pat and squish into a 7-inch square. Wrap up well and refrigerate until the dough is ready.
When dough has chilled, roll it out on a well-floured surface to a an 11-inch square. Put the butter square diagonally on the dough, so you have a butter diamond on a dough square. Fold the corners of the dough in to cover the butter and meet. Pinch the edges together. Roll this out from the center to form a 14-inch square. Fold into thirds to form a long, narrow rectangle. Then fold into thirds again the other direction to form a small square. Each of these "into-thirds" folds is called a turn; you have now turned the dough twice. Wrap and refrigerate again for 2 hours.
Repeat the rolling and folding again so you have a total of four turns, including the earlier ones. Then roll the dough out into a 20-inch square. Use a pizza cutter to cut the dough in half. You should now have two long rectangles. Cut each of these into thirds, then cut each of those thirds diagonally to form two triangles each. Roll each triangle up from the wide end to the narrow end. Place on a parchment-lined, rimmed baking sheet, curving the ends to shape. Brush with the egg wash and allow to rise for 30-40 minutes. (They don't rise much.)
Bake at 400 degrees for about 18 minutes.
