Everyone sitting has to pay. And very few vegetarian options outside of rice, a salad, and the starting side dishes. Sorry, but that's how it goes with most KBBQs. Best of luck, though!
They do have some roasted veggies that you can cook (it would be on the same grill as the meat though unless you have two) when we went it was sweet potato, onion, carrot, and green onions. Outside of that there's also the banchan (Korean side dishes) that you get at most any kbbq spot
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