In a small mixing bowl, dissolve yeast and sugar in warm water. Let stand until creamy, about 10 minutes.
In a large mixing bowl, combine the yeast mixture with the whole wheat flour, salt and one cup of the bread flour; stir well to combine. Add the remaining flour, 1/2 cup at a time, stirring well after each addition. When the dough has pulled together, turn it out onto a lightly floured surface and knead until smooth and supple, about 8 minutes.
Place into a lightly oiled bowl, and turn to coat the whole surface with oil. Cover, and let rise in a warm place until doubled, about 45 minutes.
Punch down the dough, and let rest 10 minutes. Divide into 4 balls. Place on cookie sheets, and flatten into disks. Cover and let rise until doubled, about 30 minutes. Preheat oven to 375 degrees F (190 degrees C).
Lightly beat the egg white with the water and brush the risen loaves with this mixture. Bake at 375 degree F (190 degree C) for 40 to 50 minutes. When done bread should sound hollow when thumped on bottom. Remove from oven, and let cool.
Cut a circle out of the top of each loaf, and remove that part of the crust. Either remove the soft bread beneath, or compress it to form a bowl.