Here is my version, filtered through My Korean Kitchen and Kitty's Filipino father.
Music for cooking:
MmmBop (can be altered to "bimmmbop, baby, bimmmbop, baby")
Besame Mucho (you can sing along with my beloved Cenobio: "Ses-a-me, ses-a-me, ses-a-me mucho, ses-a-me!")
Any Decemebrists song in which people do not die or live lonely lives; Joni Mitchell (the strummy years); Bare Naked Ladies.
Ingredients and equipment you will need:
A sharp knife
A big frying pan, wok, or covered omelette pan
A cutting board
Something to stir stuff with
Ginger (optional, but it makes your kitchen smell nice)
Bean sprouts (if all you can get are canned, skip this part. Canned bean sprouts are gross.)
Spinach, bok choy, or napa cabbage
Mushrooms: preferably oyster, shiitake, woodears, or anything other than those bland button things (I got two packages of "Gourmet Blend" from the local HEB.)
Beef. It can be ground, very thinly sliced sirloin or tenderloin, or mince if you're in Australia or Europe. (Mince is good enough for My Korean Kitchen, so it's good enough for us.)
Zucchini. Broccoli. Kale. Whatever. What have you got? It's all gonna get wilted later.
An egg or two.
Rice. Make more than you think you'll need.
For each quarter-pound/120 grams of beef, mix:
one tablespoon each of soy sauce and sesame oil
a teaspoon, roughly, of chopped garlic
a half-teaspoon of brown sugar
as much grated ginger as you feel is advisable (optional)
Mix it all up and either mix it into your beef mince or pour it over your very thinly sliced beef (or tofu, if you don't eat vegetarians).
(Protip: beef can be sliced more thinly than you imagine possible if you freeze it for an hour first, then use a very sharp knife.)
While this is marinating, chop up your bok choy or Napa cabbage, or slice your spinach up a bit.
Julienne (that is, cut into matchsticks) the carrot and/or zucchini.
Slice or rinse or otherwise parcel out the mushrooms you've gotten your paws on.
Chop up whatever else you've got in the way of vegetables.
Keep all these things separate. If you have actual bok choy, you'll want to cook the stems first. I got baby bok choy, so that wasn't necessary.
Take your big pan and heat up a smidge of sesame oil in it. Add some of that chopped garlic you've got hanging around.
Add the bok choy/cabbage/zucchini/spinach and cook it just until it's wilted. You don't want mush; you want things to retain their basic character.
Scoop that shit out of the pan and put it somewhere out of the way.
Put the carrot in there. Cook it for about three minutes, or until it's tender but still crunchy. Err on the side of crunchy.
If you have decent bean sprouts, dump out the carrots and put the bean sprouts in their place. Cook a minute or two, until they're just-barely tender. You should not need more oil or water; the bean sprouts have plenty of water on their own.
Now dump out the bean sprouts. You *are* keeping the veggies separate from one another, right? Good.
Add the barest squidgen of oil to the pan, turn the heat up, and add the mushrooms. You want to sear them rather than have them release all their liquid. Once they smell good, dump 'em out.
(Yes, we're using a lot of plates. It's worth it.)
Now cook your meat. What I do is pan-fry it, then drain it through a fine-mesh strainer, so all the fat goes away and all the garlic stays in the mix. You want the heat high, but not high enough to make the residual oil in the pan smoke all over the place. Eugh.
Dump out the meat. Turn the heat off under the pan.
Now here is where I diverge from real bibimbap and go to the true round-eye version. Normally, you'd be layering all this stuff atop cooked rice and topping it with chili sauce and--here is the key--a sunny-side-up egg.
I hate uncooked eggs. Plus, I have to take this shit to work and reheat it in the microwave. So I do what Kit's dad does, and scramble an egg per serving, and cook it like a flat, plain, browned omelette.
I beat that egg to death, then pour it into the pan (which is still warm from the meat) and let it set. Once it's brown, I flip it over all of a piece and let it brown on the other side. Then I take it out, chiffonade it (that is, cut it into delicate fine strips) and sprinkle it over the rest of my booty.
To serve, plate up some rice. Put portions of everything you've just cooked in beautifully-arranged order atop the rice. You can top it with chili sauce, or sprinkle sesame seeds over it, or just dig in with a side of kimchi.
I'm sure there's a formal recipe for the chili sauce, but I just use the stuff that comes in the little jars and mix it to taste with sesame oil and soy sauce. Sometimes I add some leftover garlic if I feel really bold.
And there you have it. You can make all this stuff ahead of time, cook the rice fresh, and nuke your pre-prepared ingredients, then put it all together. Or you can do what I do, which is attempt something like a Michelin chef would plate, then say "Fuck it" and mix it all together in a plastic container. Either way, it's tasty.