I don’t have a specific recommendation but korean bbq is very low carb gluten free friendly. You just order the meat/protein you want and they will bring lettuce leaves to make rolls with it. Lots of veggie options- you definitely want to bbq some mushrooms- and the pickled veggie banchan and kimchi is low carb. Usually there are some salads on the menu too, just inquire about the dressing- some do a simple sesame oil thing but others make their own salad dressing.
