01To make the endive, melt the butter in a large nonstick skillet over medium-low heat. Season the endive with salt and pepper and place cut side down in the skillet. Cook until lightly browned on the bottom, about 8 minutes.
02Sprinkle the sugar and lime juice over the top and cook, turning occasionally, until the endive are caramelized and tender when pierced with a knife, about 15 minutes longer. Cover and keep warm (can be prepared ahead and reheated in the oven).
03To make the scallops, heat the oil in a large skillet over medium-high heat. Season the scallops with salt and pepper, place them in the skillet and sear until lightly browned and warm in the center, about 1 minute per side.
04To make the sauce, combine the shallot, garlic, ginger, lime juice and port in a nonreactive saucepan over medium-high heat. Simmer until nearly all of the liquid has evaporated, about 3 minutes. Add the cream, bring to a boil and remove from the heat. Whisk in the butter a few pieces at a time until all is incorporated. Strain the sauce and season with salt, pepper and a touch of cayenne. Keep warm.
05To serve, place 1 endive half on each of 6 plates. Divide the scallops among the plates and spoon the sauce over and around them. Sprinkle with the scallions and tomato. Serve immediately.