Add yeast and sugar to 1/3 cup warm water. Set aside and allow to proof for 5-10 minutes.
Place bread flour, whole wheat flour, salt and 4 1/2 teaspoons of oil in food processor. Process for approximately 10 seconds to combine.
Add the egg and the 2/3 cup cold water to the yeast mixture and mix well.
With the processor running, add the yeast mixture through the feed tube in a slow steady stream as fast as the flour will absorb it.
When the liquid is absorbed and mixture has formed a ball of dough that has cleaned the sides of the work bowl, process for 45-60 seconds longer to knead.
Place the 1 tablespoon of vegetable oil in a large bowl. Using your fingers/hands, coat the sides of the bowl. Rub your hands with the oil to make handling the dough easier.
Remove the dough from the workbowl and place in oiled bowl. Flip dough over so it is oiled on all sides. Lay plastic wrap on top of dough to keep it from drying while rising (you should have enough oil on the top of your dough so the plastic won't cling to it).
Place dough in a warm, draft free area and allow to rise until double in bulk. I warm my oven slightly (2 minutes) and allow the dough to rise there. It is quicker. The dough has risen enough when you poke it with your finger and the indentation stays.
Once dough has risen, remove it from the bowl and punch it down. Reshape it to fit in a greased bread pan. Re-place plastic wrap (being sure you put the oiled side down) and allow to rise a second time, once again until doubled.
Preheat oven to 375`. Bake for 20-30 minutes or until your loaf is brown on top and sounds hollow when you tap it.