Yes, You Can Grill Kimchi And You Absolutely Should - Tasting Table
Briefly

Grilling kimchi adds new textures and flavors, as the sauce caramelizes to create crispy edges and infuse the cabbage with a smokey flavor.
To grill kimchi effectively, use whole leaves of cabbage, drain well, and grill for just one to two minutes for perfect char.
Read at Tasting Table
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