Preheat the oven to broil with the rack 6 to 8 inches below the lighted broiler plate.
Place the tomatoes, 1/4 cup of the olive oil, marjoram, lemon zest and 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper, and the lemon juice in a 10-inch saute pan, saute quickly, and set in the oven on the rack. Cook until the tomatoes are well caramelized, 8 to 10 minutes. Remove from the oven and allow to cool for at least 10 minutes. Add the basil to the vinaigrette and toss to blend. Set aside until ready to use.
Place the bok choy in a Dutch oven with the water and turn the heat up to high. When the water begins to boil, season the bok choy with 1 teaspoon of the salt and the 1/2 teaspoon white pepper. Place a lid on the pan and steam the bok choy until most of the liquid has evaporated and the bok choy is tender, about 6 to 7 minutes. Remove from the Dutch oven and slice each bulb in half lengthwise. Place the bok choy, cut side down, on a plate with the leaves in toward the center of the plate and the bulb ends facing towards the rim.
To cook the salmon, lay the fillets in a 12-inch saute pan and season with the remaining salt and remaining black pepper. Brush the remaining 1 tablespoon of olive oil over the salmon, arrange marjoram sprigs over top, and broil in the oven until the salmon is browned and cooked through, about 5 to 6 minutes. Remove from the oven and lay the salmon on the bed of bok choy. Top with the tomato and lemon vinaigrette.
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