In a medium saucepan, combine white wine, wine vinegar, and shallots. Cook until liquid is almost evaporated, approximately 1 tablespoon left. Stir in heavy cream and let boil down until reduced by half. Stir in butter 1 tablespoon at a time, allowing each to melt before adding the next. Keep warm while preparing the scallops.
Preheat oven on broiler setting.
Brush scallops with olive oil and sprinkle with salt and pepper. Place under preheated broiler for 2 minutes on each side, until scallops are opaque, with a bit of brown around the edges. Place a spoonful of sauce on each plate, and top with 4 scallops.