Prepare the ingredients and sauce: Lightly season the salmon and cabbage wedges with salt and pepper on both sides. In a small bowl, mix all the sauce ingredients together and set aside.
Sear the cabbage and salmon: Heat oil in a large flat-bottomed pan over medium heat. Add the cabbage wedges first, then place the salmon fillets in the pan. Let both sear without moving for 5 minutes.
Flip and continue cooking: Flip the salmon, then flip the cabbage. Cook for another 3 minutes. Remove the salmon and set aside. If your fillets are thicker than 2.5 cm (1 inch), cook them for an extra 1 to 2 minutes.
Cook the mushrooms: Add butter to the pan and sauté the mushrooms until softened, about 2 minutes. Push them to the sides of the pan.
Add the sauce and finish simmering: Return the salmon to the pan. Drizzle the miso sauce over everything, cover, and reduce the heat to low. Simmer for 2 minutes.
Garnish and serve: Garnish with sesame seeds and chopped green onion. Serve immediately with hot steamed rice.