In a alrge mixer bowl, combine 1 cup flour, yeast, sugar and salt. Heat one cup water, milk and 1/4 cup butter to 120 - 130 deg f. Add to flour mix. Add one egg and mix at low speed for 1 minute. Mix at medium speed for three minutes. Set aside. In a large bowl, cut one cup firm butter into remaining flour until butter particles are the size of large peas. Pour yeast mixture over flour-butter mixture. Fold in until all flour is moistened. Cover and refrigerate for 2 hours.

Place dough on floured board and knead about 6 times to release air bubbles. Divide into 4 parts. Roll each part to a 14 inch circle. With a sharp knife, cut into 10 pie shaped pieces. Starting at wide end, roll each wedge toward point. Place on ungreased baking sheet, point side down and curve into a croissants. Cover and let rise, in a warm place, until almost doubled in size (1 - 1 1/2 hours). Combine slightly beaten egg with one tablespoon water and brush on each croissant. Bake at 350 deg f for 15 to 18 minutes or until browned. Remove from baking sheets and cool on wire racks.