Stir together the biga ingredients (1/2 cup whole wheat flour, 1/2 cup bread flour, 2 1/4 tsp yeast, 1/2 cup warm water) in a large glass bowl until well combined.
Cover the bowl tightly and let sit at room temperature for 20 to 24 hours, the dough will expand so make sure your using a large bowl.
THE BREAD:
Add the 2 1/2 cups of bread flour, 1 tsp salt, 2/3 cup of water and the and 1 TBSP of the oil into the bowl with the biga and stir until thoroughly combined.
Knead the dough in the bowl by hand for about 5 minutes.
Form the dough into a ball then cover the bowl and set in a warm place until the dough has doubled in size, about 1 hour.
Separate the dough into 6 equal size balls then form the balls into cylinder shapes roughly 5-inches long and place them on a large baking sheet at least 2-inches apart.
Flatten the dough cylinders just a bit so theyre flat on top then sprinkle a little flour on top of the dough and let sit for about 30 more minutes.
Preheat the oven to 425°F.
Use a serrated knife to gently cut 3 shallow slits on top of each dough roll.
Place the baking sheet in the preheated oven and bake the dough for 15 minutes.
Take the breads out of the oven and brush the tops with the egg white then put the breads back in the oven and bake for 5 more minutes or until lightly browned.
Allow the rolls to cool on a wire rack for about 15 minutes before splitting.