In a large bowl, dissolve yeast in water.
Add milk, salt, sugar, egg, and 1 cup of the flour.
Beat to make a smooth batter, then blend in melted butter; set aside.
In a large bowl, using a pastry blender or 2 knives, cut the 1 cup firm butter into 4 cups of the remaining flour until butter particles are the size of peas.
Pour yeast batter over top and carefully turn mixture over with a spatula to blend just until all flour is moistened.
Cover with clear plastic wrap and refrigerate for at least 4 hours or up to 4 days.
Turn dough out onto a floured board, press into a compact ball, and knead briefly on a lightly floured board to release air.
Divide dough into 4 equal parts.
Shape 1 part at a time, leaving remaining dough, wrapped in plastic wrap, in refrigerator.
On a floured board, roll 1 part of dough at a time into a circle, 17 inches in diameter.
Using a sharp knife, cut circle into 8 equal wedges.
For each croissant, loosely roll wedges toward point.
Shape each roll into a crescent and place on an ungreased baking sheet with point down, 1 1/2 inches apart all around.
Cover lightly and let rise at room temperature in a draft-free place. (Do not speed rising of rolls by placing them in a warm spot.) When almost doubled (about 2 hours), brush with egg-water mixture.
Bake in a 325° oven for about 35 minutes or until lightly browned.