1. Measure the flour into a mixing bowl. Remove 1/2 cup and set it aside in another bowl. Take the half stick of chilled butter, cut it into small pieces, and drop it into the flour. With two knives, a pastry blender, or your fingertips, cut or rub the butter into the flour until it resembles cornmeal.
  1. Add water to the flour. Mix gently with a fork until you have a rough dough that pulls away from the sides of the bowl. If you need to add more water, do it a tablespoon at a time, until the dough holds together.
  1. Turn the dough out onto a lightly floured surface and knead until it is smooth and the gluten has been somewhat developed, about 2 or 3 minutes. Pat the dough into a 9" square and wrap in plastic. Refrigerate for at least 30 minutes.
  1. Take the remainder of the butter and the reserved flour and mix the two together until they're well blended and smooth. You can do this with a mixer, a food processor or with a spoon, by hand. Pat this butter/flour mixture into an 8" square on a lightly floured piece of waxed paper. Cover it with second sheet of waxed paper and refrigerate it for at least 30 minutes.
  1. Remove the dough from the refrigerator and put it on a lightly floured surface. Gently roll it into a square about 12" on each side. You don't have to be obsessive about the dimensions, but come pretty close.
  1. Put the chilled butter in the center of the dough as shown. Fold the corners of the dough over the butter until they meet in the middle. Pinch and seal the edges of the dough together.
  1. Turn the square over and tap it gently with your rolling pin or by hand into a rectangular shape. (Make sure everything is still completely, but lightly, floured.) Roll the dough into a larger rectangle, 20" x 10". As you work, keep the dough, the table, and the rolling pin well dusted with flour. Turn the dough over from time to time to keep the layers even.
  1. When the dough is the right size, brush any excess flour off the top, and fold the bottom third of the dough up to the center and the top third over (like a business letter). Line the corners up as neatly as you can; dab them with a little water to help them stick together if necessary, and turn the dough package 1/4 turn to the right so it looks like a book ready to be opened. If the dough is still cold and relaxed, do another rolling and turning the same way. (If it begins to feel too soft or wants to resist being rolled, cover it, put it on a small baking sheet, and refrigerate it for 15 minutes to chill and relax.)
  1. If you've successfully rolled it out and folded it twice, you've completed two turns. Classic puff pastry gets six. Continue refrigerating it after each two turns (or more often if necessary) until all six turns are completed. Keep track of how many turns you've made.
  1. When all six turns are done, put the dough in the refrigerator for at least an hour (and preferably overnight) before shaping.
  1. On a lightly floured surface, roll the dough until it's a rectangle about 12" x 18". Trim 1/4" off the edges of the dough all the way around with a very sharp knife or a pizza wheel. This cuts off the folded edges which would inhibit the "puff."
  1. Using half the dough at a time, roll each piece again into a 12" x 18" rectangle. Square the edges of the dough on every edge using a ruler and pizza wheel. Cut the dough in thirds lengthwise and in half through the middle. This will give you six 4" x 9" pieces. Cut each piece in half diagonally, and arrange them so the points of the triangles are facing away from you. It's okay to stretch them out gently to elongate them when you do this. Cut a 1/2" notch in the short edge of the triangle.
  1. If you want to, this is the time to place a teaspoon of filling at the base of the triangle. Roll up the dough, starting with the notched edge and working toward the point. Make sure the point is tucked under the bottom of the croissant. If you have to stretch the dough a little to make that happen, it's OK. You can also use a drop of water on the tip to help it stay in place. Form the crescent by bending the ends toward the center where the tip is tucked underneath. Place the croissants on a lightly greased or parchment-lined baking sheet. Cover and chill for 30 minutes. You could also freeze the unbaked pastries at this point.
  1. Fifteen minutes before you want to bake the croissants, preheat your oven 425°F. Just before they go into the oven, brush the tops with egg wash (1 large egg beaten with 1 tablespoon cold water). Bake for 15 minutes. Reduce the heat to 350°F and bake for another 10 to 15 minutes. Remove from the oven and cool completely on a rack.