In bowl, combine sugar, salt, yeast, and i cup flour. In saucepan, heat oil and water until very warm. With mixer at low speed, beat liquid into dry ingredients. Beat at medium speed for 2 minutes. Reserve 1 egg yolk. To mixture in bowl, add egg white, other eggs, and 1 cup flour. Beat 2 minutes. Stir in 1¼ cups flour.
On floured surface, knead until smooth and elastic, about 10 minutes, working in about ¼ cup flour. Shape dough into a ball and place in a greased bowl, turning dough to grease top. Cover and let rise in warm place until doubled. about 1 hour.
Punch dough down; turn onto floured surface; cover; let rest 15 minutes. Cut two-thirds of the dough into three equal pieces. Roll each piece into a 13-inch rope. On greased large cookie sheet place ropes side by side and braid - just like hair would be braided. Pinch ends to seal. Cut remaining dough into three pieces. Roll each into a 14-inch rope. Braid as above. Place small braid along center top of large braid. Tuck ends under to seal and keep braid in place. Cover with a towel and let rise until double in size. Preheat oven to 375 degrees F. In cup, beat the egg yolk; use to brush loaf. At this point, if you like, poppy seed may be sprinkled on top of the braid. Bake 30 minutes or until golden brown. Loaf sounds hollow when tapped.
Yield: 1 loaf - 16 servings.