In a small bowl, mix all of the mushroom rub ingredients until well combined.
Slice off the head of each mushroom, as well as, the pointy stub on the opposite end. Discard each stub and save the mushroom heads for future meals.
Rub the mushrooms with the prepared rub, covering each mushroom completely.
If using the panini grill: Heat the panini grill to medium. Once hot, add the mushrooms and close the lid. Grill the mushrooms for 30 minutes, stopping every 5 minutes to flip and rotate the mushrooms to ensure even grilling.
If using cast iron skillets: Heat one of the skillets on the stovetop over medium heat. Once hot, reduce the heat to medium-low and add the mushrooms, then top the mushrooms with the second skillet to press. Leave the mushrooms pressing for 20 minutes, stopping every 5 minutes to flip the mushrooms.
Preheat the oven to 350°F.
Brush the bottom of a baking dish with Korean BBQ sauce, then add your pressed mushrooms to the dish. Brush each side of the mushrooms with more sauce.
Once the oven is preheated, add the baking dish to the oven and bake the mushrooms for 35 minutes.
Before serving, brush each mushroom with additional sauce. If desired, sprinkle with toasted sesame seeds and/or sliced green onions.
