Cut out the core of the cabbage, leaving a 2- to 3-inch hollow in the base. Place head, stem-side up, in a large stockpot; pour in 1 to 2 inches of water. Cover and bring to a boil over high heat. Steam until leaves come off easily, about 3 minutes. Peel off 2 leaves large enough to wrap your fillets; let cool.
Preheat the oven to 450 degrees F (230 degrees C). Grease a baking dish with butter.
Season halibut with salt and cayenne on both sides. Lay cooled leaves flat on your work surface. Center fillets over each leaf. Divide ginger, Fresno chile, and green onions over fish. Spoon soy sauce on top; sprinkle with sesame oil and seeds.
Fold the stem side over each fillet. Fold in the sides and wrap the leafy end on top. Tie fish with string if desired. Transfer to the prepared baking dish, seam-side up.
Bake in the preheated oven until fish flakes easily with a fork, about 15 minutes. Let sit for 5 minutes.
Mix 2 tablespoons butter and miso together. Snip off the string and transfer fish to a shallow bowl. Spoon pan juices on top, unwrap cabbage, and top with miso butter.