❓What do I do when every company team-building dinner is at a Korean BBQ place?

Honestly, you won't go hungry at a BBQ place as a vegetarian — most of them have options you can grill yourself, like enoki mushrooms, king oyster mushrooms, rice cakes, corn, grilled tofu, and lettuce. Just tell the organizer ahead of time, "I'm vegetarian, could you order a few mushroom and vegetable dishes," and people generally won't think it's a hassle. If you're worried about not getting full, eat something small beforehand, then at the dinner focus on the mushrooms, vegetables, rice, and the social side of drinks and conversation — the point of these dinners is really the gathering itself, not eating until you're stuffed. If you run into this kind of situation often, it also helps to give a heads-up to coworkers you're close with beforehand — a lot of the time people will proactively help make sure the right dishes get ordered.