Combine the soy sauce, brown sugar, and 1 tablespoon of the sesame oil in a large bowl. Cut the salmon portion in half and place both halves in the bowl (fleshy side down, if skin-on salmon). Let the salmon sit in the marinade for about 30 minutes.
In a large sauté pan, heat 1/2 tablespoon of the remaining sesame oil over medium heat. Fry the salmon, skin side down. Pour the marinade over the salmon and cook for about 5 minutes, then move the salmon to one side of the pan. Pour in the remaining 1/2 tablespoon of sesame oil and sauté the ginger and mushrooms, pushing them around the pan so they mix with the salmon marinade and fat coming off the salmon. After about 3 minutes, or until the mushrooms are nearly cooked to your liking, add the green garlic or garlic and saute for 1 minute. Add the pea shoots and cook until wilted. Be sure to stir the vegetables so they are all coated in the salmon marinade.
Once the pea shoots are wilted, the salmon should be done. (If not, remove the vegetables from the pan and set aside till the salmon is cooked to your liking). Remove salmon from pan, place on a plate skin-side down, and top each salmon half with a bit of vegetables and the garnishes, if you'd like! The salmon should be nicely glazed and have sweet, salty, sesame, and ginger flavors!