Dissolve yeast in warm water in large bowl. Add oil, sugar and whole wheat flour. Mix until smooth. Let sponge rest 20 minutes. Mix down; add 3/4 cup Parmesan, salt, garlic powder, basil and oregano. Stir in enough bread flour to make dough easy to handle.
Knead until smooth and elastic, about 10 minutes. Shape into two rounds. Place dough on greased baking sheets. Cover and let rise in warm place until doubled in size, about 45 minutes. Whisk together egg and water and brush over each loaf. Sprinkle each loaf with 2 tablespoons Parmesan cheese.
Bake in preheated 350°F oven for 30 to 35 minutes. Cover with foil for last 10 minutes to prevent over-browning. Remove from baking sheets. Cool on wire rack.