Combine carrot, shallot, ginger, garlic, wine and broth in a medium sauce pan. Cook, uncovered, over medium heat 12 minutes or until liquid is reduced to about 1/2 cup. Strain; discard vegetables and reserve liquid.
Pat scallops dry with a paper towel. Heat oil in a nonstick skillet that has ben sprayed with nonstick cooking spray over medium-high heat. Place scallops in single layer in pan. Cook until golden brown on bottom, about 4 minutes. Turn scallops. Sprinkle with salt and pepper and cook about 2 minutes until second side is lightly golden.
Reduce heat to low and pour reserved liquid over the scallops. Simmer 1 minute or until scallops are done, stirring any browned particles into sauce and spooning sauce over scallops.
To serve, arrange scallops on deep platter and spoon sauce over them. Sprinkle with chives.