Dear World. Here is a recipe for happiness. You're welcome.
3/4 cup water, warm
3 tablespoons butter, melted
3 eggs, whipped
1/3 to 1/2 cup sugar, depending on how sweet you like it
1 tsp salt
4 cups flour
1 tablespoon yeast
If you have a bread machine, dump all these ingredients in the mixer (put the yeast in a hollowed out hole in the flour so it doesn't get wet if you want to used timed-start), put on the dough cycle, and let it all mix and rise. Also skip this next section.
If you don't have a bread machine, mix warm water, yeast, and an additional tsp of sugar in a separate bowl to foam and rise. In large bowl or kitchen aid, mix butter, eggs, sugar, and salt. Slowly add in the flour, 1/2 at a time, alternating with the foamed yeast/water mixture. If using a kitchen aid, you can switch to the dough hook after adding the first two cups of flour. Mix almost all of the last cup of flour in, but reserve some (probably about 1/3 cup or 1/4, I'm actually not sure because I never make less than a triple batch of dough when making it by hand) to flour your counter with and kneed in by hand. Kneed in that last but of flour until the dough has a smooth, elastic feel. Set in greased bowl and cover with a dish cloth, to rise until doubled.
Now both our bread machine/by hand peeps join up again. When it's risen, kneed on a floured surface for a few minutes to kneed out air hole pockets. Divide in half and cut them into either 3 or 4 strands, depending on the braid you're using (or more strands, if you wanna get really fancy) Let the pieces set for five minutes, then roll them into long "snakes" and braid. Put both loaves on a greased cookie sheet, and let rise till doubled. Brush with 1 egg yolk mixed with about 1 tablespoon of water (pastry brushes are your friend, paint brushes not so much) to make a lovely shiny glaze. Bake at 375 for 8 minutes, cover loosely with foil, and bake for another 8 minutes.
Let cool on baking racks or a wooden serving plate (if you leave it on the baking sheet too long the bottom gets gummy, it's gross), for about 10 minutes or so, but you should probably eat it warm. Gwen would tell you that it's better still-fresh-but-not-warm, but she would be wrong. Tear off large chunks,* lather in butter, and enjoy!
*This step is highly important. Whatever you do, do NOT cut challah. 1) it tastes better torn (it's a scientific fact, practically. Anyone with halfway decent taste buds agrees) 2) Cutting it goes against the Jewish tradition, based on prophecy that swords will be turned into plowshares (Isaiah 2:4) 3) IT'S SACRILEGE. It just goes against all the sacred rules of challah, ok?