Combine ¼ cup all-purpose flour, ¼ cup warm water, the yeast, and 1 tablespoon sugar. Let stand at room temperature for 10 to 15 minutes or until the mixture begins to bubble.
Meanwhile, stir together 2 cups all-purpose flour, the remaining 1 tablespoon sugar, and the salt in a large bowl. Add the remaining 2¼ cups warm water, the yeast mixture, oil, egg, and egg white. Beat with an electric mixer on low to medium speed for 30 seconds, scraping the side of bowl constantly. Beat on high speed for 3 minutes. Using a wooden spoon, stir in whole-wheat flour and as much of the remaining all-purpose flour as you can.
Turn out dough onto a lightly floured surface. Knead in enough of the remaining all-purpose flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Cover the dough and let rest for 10 minutes; knead for 2 minutes more. Cover the dough and let rest again for 10 minutes; knead for 2 minutes. Coat a very large bowl with cooking spray; add the dough and coat the top with nonstick cooking spray. Cover and let rise in a warm place until double in size (about 1 hour).
Punch down the dough; cover and let rise a second time for 45 minutes. Punch down the dough; divide into two portions. Cover and let rest for 10 minutes. Divide each portion into three ropes (if making loaves) or 16 pieces (if making rolls). For loaves, roll each dough portion on a lightly floured surface into a 14-inch-long rope. Place the ropes on a very large baking sheet lined with parchment paper. Using three ropes for each loaf, braid the ropes into two loaves. Be sure the braids are at least 5 inches apart. For rolls, coat two 13x9-inch baking pans with cooking spray; shape the dough portions into rolls and place 16 rolls in each pan.
Cover the loaves or rolls and let rise in a warm place until nearly double in size (30 to 45 minutes). Preheat the oven to 425°F.
Combine egg yolk and the 1 tablespoon water in a small bowl; brush atop the loaves or rolls. Sprinkle with poppy seeds, sesame seeds, and/or oats.
Bake the loaves for 10 minutes. Reduce oven temperature to 375°F. Bake for 15 to 20 minutes or until the bread sounds hollow when tapped. (For rolls, bake at 425°F about 15 minutes or until the roll tops sound hollow when tapped. Do not reduce oven temperature.) Remove from pans or baking sheets and cool on wire racks.
Tip: If using a sugar substitute, we recommend Splenda Granular or Sweet 'N Low bulk or packets. Follow package directions to use product amount equivalent to 2 tablespoons sugar. Nutrition Per Serving with Substitute: same as below, except 114 cal., 20 g carbo., Carb choices: 1.