In a large mixing bowl, combine the 1/2 cup warm water and the yeast. Let stand for 5 minutes or until the yeast dissolves.
Stir milk, margarine, sugar, salt, eggs, and egg yolk into yeast mixture. Add 2 cups of the flour and beat well. Using a wooden spoon, stir in as much of the remaining flour as you can.
Turn out onto a lightly floured surface and knead in enough of the remaining flour to make a moderately soft dough that's smooth and elastic (3 to 5 minutes total).
Shape dough into a ball. Place dough in a lightly greased bowl, turning once to grease the surface. Cover and let rise in a warm place until doubled (about 1 hour).
Punch the dough down; turn out onto a lightly floured surface. Divide the dough into 6 equal portions. Cover and let the dough rest for 10 minutes.
Roll each portion of dough into a ball. Roll each ball into an evenly thick rope about 16 inches long. Line up 3 of the ropes, 1 inch apart, on a greased baking sheet. Starting in the middle, braid by bringing left rope underneath center rope; lay it down. Then, bring right rope under new center rope; lay it down. Repeat to end. Starting at the middle again, braid the other end by bringing outside ropes alternately over center rope. (Braid the ropes loosely, so the bread has room to expand.) Press rope ends together to seal. Repeat braiding with remaining three ropes for a second braid. Cover the braids and let rise until almost doubled (about 30 minutes).
Combine egg white and the 1 tablespoon water. Brush top of dough with egg-white mixture. Bake in a 375 degree F oven for 25 to 30 minutes or until done. Cover with foil the last 10 minutes, if necessary to prevent overbrowning. Remove from baking sheets; cool. Makes 2 loaves.
Chill one braid while baking the other to prevent dough from overrising.