1/2 cup orange juice
1/4 cup water
1 Tbsp. active yeast
1 large egg
2 large egg yolks
1/3 cup olive oil
1/3 cup honey (this makes for a challah with a pronounced sweet edge - you can cut it down if you want something more neutral, but it's lovely as it is)
1 tsp coarse salt
2 cups whole wheat flour (if you're not a fan of whole-grain breads, you can use all white flour instead)
~2 cups bread flour
1 egg, lightly beaten with a splash of water (henceforth known as the egg wash)
Pour the orange juice and water in the bowl of a stand mixer, then sprinkle in the yeast. Let sit ~5 minutes, to allow the yeast to soften and bloom.
Add the egg, egg yolks, oil, honey and salt. Fit the mixer with a whisk attachment, and mix until the liquid is well-blended. Add the whole wheat flour, mixing until it forms a batter.
Remove the whisk attachment, and fit the mixer with a dough hook. Add the white flour, bit by bit, until a soft and sticky dough is formed that just clears the sides of the mixing bowl, but still sticks to the bottom. Continue kneading with the dough hook for a few more minutes, to form supple, sticky, and well-developed dough.
Lightly oil a large bowl, and turn the dough out into it. Swish it around, then flip it over, so that the top is oiled as well. Cover the bowl, and let rise until doubled, ~1-2 hours, depending upon the temperature of the room. When risen, punch it down to deflate (I like to flip it over at this point, but it's not necessary), and let rise another half hour to an hour, until it begins to rise again. The dough can be refrigerated overnight for either of these rises -- just remove it and give it an hour to come to room temperature before proceeding with the recipe.
After the dough has risen for the second time, line a baking sheet with parchment or dust it with cornmeal. Divide the dough into strands and weave it into a braid of your choosing -- you can do a standard three-strand braid, tucking the edges under, or search the internet for an ornate braiding method of your choosing. Brush the dough with the egg wash (a brush is best for this, but I've made do with my fingers at times), and let it rise until its increased at least by half, ~45 minutes to 1 1/2 hours, depending upon the room temperature.
While the dough is rising, preheat the oven to 375 degrees farenheit.
When the dough has completed its final rise, give it another brush with the egg wash (be delicate to avoid deflate all that nice rising that's just happened). Bake until the bread is burnished to a dark brown and smells done, ~30-45 minutes. Transfer to a rack, and allow to cool fully before slicing.