Starting at the base of the cabbage, slice only the pale-green parts into ½ inch ribbons. Set the leafy-green parts aside and use at another time for a salad or slaw.
Thoroughly pat the salmon dry and generously season the flesh side with sea salt.
Mix together the scallions, ginger, 2 tablespoons oil, 1 teaspoon soy sauce, vinegar, and ¼ teaspoon sea salt in a bowl. Add more salt, if needed. Let it sit for at least 15 minutes to let the flavors come together.
In a large skillet over high flame, heat 2 tablespoons oil until hot. Place salmon, skin side down, in skillet and cook for a minute or two until skin sizzles and gets brown.
Using a spatula and a pair of tongs, carefully flip the fish so skin side is up. Turn off heat and let heat remaining in skillet gently cook the second side. Once fillet has stopped sizzling, carefully transfer to a plate. Return pan to medium-high heat and add the cabbage and garlic. Cook, tossing occasionally, until cabbage is wilted and browned in some spots, about 5 minutes. Stir in 2 teaspoon soy sauce and cook until evaporated.
Divide cabbage between two plates and top with salmon and ginger scallion sauce.