Melt 2 tablespoons butter in a large skillet over medium-high heat. Sprinkle in the sugar and cook until it just turns golden.
Add the cabbage and 1/2 teaspoon salt, cover and cook until wilted, about 5 minutes. Add the broth and continue cooking, covered, until crisp-tender, another 15 minutes. Preheat the broiler to high.
Transfer the cabbage to a flameproof casserole dish. Wipe out the skillet, then add the remaining 6 tablespoons butter and melt over medium heat. Brush the scallops with some of the butter and season with salt and pepper; arrange in a single layer over the cabbage in the casserole dish and broil until firm, 5 to 7 minutes.
Meanwhile, continue cooking the butter over low heat, swirling the pan occasionally, until toasted and fragrant, 5 minutes. Add the capers, raisins and vinegar (be careful - the butter may foam and bubble); swirl the pan until the raisins are plump. Season with salt and pepper.
Divide the scallops and cabbage among plates. Add the parsley to the sauce and spoon over the scallops.