Just had the fortune to enjoy it in C on ICN-SEA. (How I got to snag a C seat is a whole 'nother story.

) As a native Korean, I can say that this is virtually the same as many restaurants in Korea serve Ssambap, except of course for the quantity.
Those 'weird, odd' vegetables are considered as 'upscale' versions of your run-of-the-mill red-leaf lettuce.

And supposed to be better for your health, stamina and whatever else you can think of, not to mention better tasting. (Hey there, why are you smirking?

)
As to how I eat it, I prefer to have some meat, a slice of raw garlic (not served in Asiana version, for the obvious reason I guess -- too bad

) and Ssamjang (that brown paste) on a couple of different veggies, wrap it, chew a couple times without rice to savor the flavor, and then finally let rice join the others in my mouth. And maybe finish it with a piece of chili (be careful, it can be quite hot) with ssam-jang, rinse my tongue with a spoonful of the soup, and repeat until there's nothing left.
I think someone else already mentioned this in another thread, but Ssambap seems to be served only on ex-ICN flights. On my particular flight, the menu indicated that SEA-ICN serves Bibimbap instead of Ssambap. (in C)
Oh, and the menu also mentions than you can request a snack between the two meals. I asked for a bowl of wonton soup when my seatmate asked for a bowl of ramyun. All I can say is: try either, you won't regret it! Wonton soup has shrimp-and-pork wontons in clear bonito soup. Ramyun (or ramen) seemed to be the usual stuff popular in Korea. Not the pour-hot-water-and-wait stuff, but properly cooked -- though from a packaged instant noodle. Other options I think were salad, sandwich, and maybe one more thing I don't remember.
Nitpicking for a moment, (ignore the rest if you're not interested in trivia) those leaves with jagged-edge
stupidhead referred to as "sesame-leaves" are actually "perilla-leaves". Since the Korean words for sesame and perilla are similar (direct translation of the Korean word for sesame (Chamkkae) would be "true sesame" while that for perilla (Deulkkae) would be "field sesame" or "wild sesame") but almost nobody other than Koreans (and maybe Japanese) consume perilla as food, not to mention that the word perilla is not as well known as sesame, many Koreans find it simpler to refer to Kkaennip (perilla leaf) as "sesame-leaf".