1. In the bowl of a heavy-duty mixer fitted with a dough hook, place yeast, sugar and three cups water. Let sit for five minutes if using fresh yeast. Add flour, salt, honey and eggs and the rest of the water. Mix for one minute and add oil.
2. Mix for 10 minutes on the highest setting. Cover the bowl and let rest for five minutes. Uncover and mix again on high for five minutes.
3. Coat your hands with oil and remove dough from mixer (dough may be somewhat sticky — this is fine). Let rise for one to one and a half hours in a closed plastic bag, leaving room for the dough to grow. (You may also want to put a bit of flour into the plastic bag and shake it before putting the dough into it.)
After dough has risen, perform hafrashas challah — separating a small amount of dough in fulfillment of the mitzvah. (Learn more about hafrashat challah.) Divide dough into sections and braid. Place loaves on Gefen Parchment-lined baking sheets, not touching each other. Cover and let challah rest for another half hour.
5. Preheat oven to 400 degrees Fahrenheit. Mix the ingredients for the egg wash and brush the challos.
6. Bake for five minutes at 400 degrees Fahrenheit, then lower to 220 degrees Fahrenheit for 10 minutes, followed by 375 degrees Fahrenheit for 25 minutes. This creates challah with a crispy crust that is soft inside.
Notes: It will also work if you start at 400 degrees Fahrenheit and, after five minutes, lower to 350 degrees Fahrenheit for another 40 minutes.