Combine the soy sauce, mirin, sake, miso, brown sugar, ginger paste, and garlic paste in a bowl. Set aside.
Season the salmon with salt and pepper on all sides. Spray a pan with non-stick spray over medium-high heat. Saute the salmon until each side turns golden.
Remove the salmon from the pan and set aside. In the same pan, add additional non-stick spray and saute the onion, carrot, mushrooms, and green onions for 4 minutes, or until they soften.
Add the napa cabbage and saute, covered for another 5 minutes.
Add the sauce and mix together with the vegetables. Top with the salmon pieces and top each with butter. Cover and cook for 5 minutes. Serve with rice.