Combine the butter, mustard, parsley, garlic paste, lemon juice, paprika, salt, pepper, and cayenne in a medium bowl. Stir together until well blended and the seasonings are thoroughly mixed throughout.
For butter dip: Melt the mixture in the microwave for a few seconds or heat it over low heat on the stovetop until fully melted.
For compound butter: Transfer the mixture to a piece of plastic wrap and roll tightly into a small log, pressing tightly as you wrap. Chill for at least 2 hours to firm. Keep refrigerated until ready to use.