Sprinkle yeast and 2tbsp sugar in water. Whisk and set aside until the mixture gets very frothy.
In the bowl of a stand mixer or a large mixing bowl, combine flours, salt and remaining 2tbsp sugar. Mix well.
Make a well in the center and add the egg replacer mixture, oil and yeast mixture. Mix and knead until a smooth, pliable dough forms. Add more flour if the dough looks too sticky. Knead for 6 minutes in a stand mixer or for 10 minutes with hand.
Transfer the dough to a greased bowl and set aside to rise for 1½ - 2hours until dough is doubled in volume.
Punch the dough lightly and divide into 3 equal portions. Form each portion into rough logs and set aside covered for 10 minutes.
Roll each log into 18" long log. Place the 3 logs next to each other. Squeeze the ends together at the top and tuck inside. Then start braiding - over 1, under 1 - just as you would with your hair. Make a fairly tight braid. Cover loosely with a greased plastic wrap and set aside to rise and get puffy, for another 1 hour.
By the end of the rising time, preheat the oven to 375°F.
Bake the bread for 20 minutes. Then tent the bread with foil and bake for 8~10 minutes until the crust is golden brown. Bread should register 190°F internal temperature.
Remove from the oven and transfer the bread onto wire rack to cool. Slice once the bread is lukewarm and enjoy.