Heat broiler. In a small bowl, combine the honey and 1 teaspoon of the soy sauce.
Place the salmon on a foil-lined broiler-proof baking sheet and season with ½ teaspoon salt and ¼ teaspoon pepper. Broil for 5 minutes. Spoon the honey mixture over the salmon and broil until the salmon is opaque throughout, 2 to 5 minutes more.
Meanwhile, heat the oil in a large skillet over medium-high heat. Add the bell pepper and cook, tossing occasionally, until just tender, 3 to 4 minutes; stir in the ginger.
Add the spinach and ½ teaspoon salt and cook, tossing, until just wilted, 2 to 3 minutes. Add the remaining 2 teaspoons of soy sauce. Serve with the salmon and sprinkle with the sesame seeds.