1Place warm water, sugar, honey, vegetable oil, salt, 2 eggs, flour and yeast in the pan of the bread machine in the order recommended by the manufacturer. Select Dough cycle; press Start.
2After the machine is done, take the dough out, and place it on a very lightly floured board, punch the dough down, and let rest for 5 minutes.
3Divide the dough in half. Then divide into 3 equal pieces, roll into ropes about 12 to 14 inches, and braid into a loaf. Do the same with the remaining other half. Gently put the loaves on a greased cookie sheet, mist with water, cover loosely with plastic wrap, and let rise for 1 to 1 1/2 hours in a warm, draft free place, until double in size.
4Preheat oven to 350 degrees F (175 degrees C). In a small bowl, beat together 1 egg and 1 tablespoon water.
5Brush risen loaves with egg mixture. Bake in preheated oven for about 20 to 25 minutes. If it begins to brown too soon, cover with foil.
Aluminum foil can be used to keep food moist, cook it evenly, and make clean-up easier.