Combine the soy sauce, ginger, brown sugar, and orange zest in a zip-top plastic bag. Add the fish and marinate 20 minutes (or longer in refrigerator). Remove the fish; reserve marinade.
Heat the vegetable oil in a large nonstick skillet over medium-high heat. Add the fish and cook 3 minutes, without turning. Reduce heat to medium, turn the fish, and cover. Cook 3 minutes or until just cooked through. Transfer to a plate, cover with foil, and keep warm.
Return the skillet to the heat. To make glaze, pour the marinade into the skillet and bring to a boil. Simmer 1 minute. Transfer to a bowl and cover with foil. Wipe out skillet with a paper towel.
Return the skillet to medium-high heat. Add half the basil, salt, pepper, garlic, spinach, and 3 tablespoons water. Cover and cook 2 minutes, or until the spinach is wilted. Transfer to a bowl and repeat with remaining basil, salt, pepper, garlic, spinach, and water. Combine with other spinach and toss with sesame oil.
Divide the greens among 4 plates. Top with the salmon, drizzle with glaze, and serve.