1/2 cup plus 2/3 cup warm water
2 tablespoons dry yeast
1 tablespoons plus 3/4 cup sugar
5 large eggs
3/4 cup vegetable oil
2 teaspoon salt
6 cups (about) all-purpose flour
1 large egg yolk
1 tablespoon water
Combine 1/2 cup warm water, yeast and 1 tablespoon sugar in large glass measuring cup and stir until yeast dissolves. Let yeast mixture stand at room temperature until foamy, about 10 minutes.
In large bowl of heavy-duty mixer fitted with whisk attachment, beat 5 eggs until blended. Add oil, salt and 3/4 cup sugar and beat until pale yellow and slightly thickened, about 4 minutes. Beat in 2/3 cup warm water. Add yeast mixture and beat until blended. Remove whisk and fit mixer with dough hook. Add enough flour 1 cup at a time to form smooth dough, beating well after each addition. Beat on medium speed until smooth and elastic, about 5 minutes, adding flour by tablespoonfuls if sticky. Turn out onto floured surface and knead 2 minutes.
Lightly oil large bowl. Add dough, turning to coat with oil. Cover with plastic wrap, then with clean kitchen towel. Let dough rise in warm draft-free area until doubled in volume, about 1 hour.
Punch down dough. Cover with plastic and clean kitchen towel and let rise 30 minutes.
Grease 2 large baking sheets. Turn out dough onto lightly floured surface. Divide dough into 2 equal portions. Divide each portion into 3 equal pieces. Roll each piece into 20-inch-long rope. Braid 3 ropes together; pinch ends together to seal. Repeat with remaining dough pieces, forming 2 braids. Place each braid on baking sheet. Cover with towel . Let rise in warm area until almost doubled, about 30 minutes.
Preheat oven to 400°F. Whisk yolk with 1 tablespoon water to blend. Brush dough with egg mixture. Bake 10 minutes. Reduce oven temperature to 350°F. Bake until bread is golden brown and sounds hollow when tapped on bottom, about 35 minutes. Transfer loaves to rack and cool.