Serve this compound butter with seafood, or as a spread for bread or baked potatoes.
Process shallots in food processor until finely chopped. Add butter; process until well blended. Add remaining ingredients. Pulse until basil is finely chopped and evenly distributed.
Roll mixture into a 1-inch log on wax paper. Wrap and chill until firm. Cut into 1/4-inch slices. Place a slice on each serving of fresh, cooked fish.