These butters are particularly appropriate for grilled or roasted fish, meats, and birds. With a crisp duck skin or perfectly grilled lamb chop, for example, a liquid sauce would destroy their effect by making the cooked surface soggy.
Simple butters have one or two elements, like anchovies, caviar, tarragon, mustard, paprika, or pistachios. Compound butters—such as Bercy (shallots, parsley, marrow), and the great Montpellier butter— have several ingredients or more than one step in the making.
The classic maître d’hôtel butter is a “simple” one of chopped parsley, lemon juice, salt, and pepper mixed to a creamy texture and divine on grilled sole. It becomes a “compound” butter if you mix in chopped tarragon leaves and meat stock reduced to a syrup with Madeira.