Step 1

Preheat your grill or oven to 500°F. (You will want whichever of those methods you choose to be very hot.)

Step 2

Remove loose outer leaves from cabbage, and trim stem to nearly flush with bottom of cabbage. Cut cabbage into 4 equal wedges, keeping core intact. Place cabbage, cut side down, in a cast-iron skillet large enough to hold cabbage in 1 layer. Drizzle vegetable oil over cabbage, and flip it around to evenly coat the cabbage with oil. Season cabbage with salt. Place skillet either on the grill or in the oven; cover (or close oven door) and cook at 500°F, undisturbed, for about 15 minutes. Flip cabbage wedges, and continue to cook until both sides are well charred, 7 to 10 minutes. (If using the oven, cook, undisturbed, until well charred and tender, about 35 minutes.) Check to see how the cabbage is doing; it should develop a nice dark sear on sides that are in contact with the pan, nearly black. Insert a small knife or metal skewer into cabbage to see if it is done cooking. You want to feel very little resistance. When it is ready, the cabbage should have a silky, yielding quality.

Step 3

As the cabbage cooks, heat butter, vinegar, ssamjang, water, and fish sauce in a small saucepan over medium-high until it just barely simmers, about 3 minutes, stirring often. Remove from heat, and set aside.

Step 4

Once cabbage is cooked, transfer it to a cutting board. Carefully cut out the core, and divide the leaves evenly among 4 bowls. Spoon ssamjang butter evenly over cabbage, and top with fried shallots, nori, and gochugaru.