Melt the butter in a large skillet over medium-high heat.
Season tilapia with pepper and quickly sauté (2 to 3 minutes per side); remove from skillet and keep warm. Add lime juice and wine (or broth) to the skillet and quickly whisk up all of the browned bits from the bottom of the pan. Bring mixture to a boil then add chicken broth, half and half, gingerroot and cayenne pepper.
LOWER HEAT IMMEDIATELY OR SAUCE WILL BREAK! Cook over medium heat for about 2 minutes, stirring constantly. When sauce has thickened, taste it and correct the seasonings if necessary.
Serve sauce over tilapia and enjoy!