2 tsp yeast
3 1/2 cups all purpose flour (I use King Arthur, which is fairly high gluten)
1/4 cup warm water
3 large eggs
1/4 cup vegetable oil
3 tbsp honey
1/2 tbsp salt
Optional egg wash:
1 egg
2 tbsp water
Combine the yeast, water, and 1/2 cup flour in your mixer bowl, and let it sit for half an hour. Add the eggs, oil, and honey, and stir until it is combined; it'll be lumpy at this point. Our in the rest of the flour, and the salt, and mix (with the paddle, if you're using a Kitchen Aid mixer) until all the ingredients are well combined. Switch to the dough hook, and kneed for about 2 minutes (or kneed by hand). This is a fairly dry dough; it shouldn't be very sticky. Add a bit more flour if it is.
Put in an oiled bowl, and let it rise for about two hours. It can go for as much as four hours with no problem, or as little as one hour if your kitchen is warm and you're in a hurry, or rise overnight in the fridge. Shape the braid. I divide the dough into six pieces, and let them rest for five minutes or so. Using a rolling pin, roll each one out to a long thin rectangle (maybe 4" by 10"). I do this on a Silpat, so I don't need to add very much flour at all to keep it from sticking. Roll the rectangle up into a long thin rope, tapering it slightly at each end.
Line a cookie tray with parchment paper (or the silpat). On the cookie tray, braid the six strands, either into two small challahs or one large one. Here are instructions for a six-strand braid; there's a You-tube video here that shows someone making the same braid, although with slightly different directions (the braiding starts about 2 inutes into the 6 minute video).
Now cover the challah with a kitchen towel, and let it proof for another 2 hours or so. (You can cut this short if you need to.) About 15 minutes before you're ready to bake it, preheat the over to 325 (yes, it's a very cool temp. for bread baking). Beat the remaining egg and water, and brush the egg wash over the challah; you could sprinkle sesame or poppy seeds on it now. Bake for about 25 - 30 minutes.