Finishing a Sauce
To add a bit of fat and additional flavors right at the end of the cooking process to round out flavors and ensure the sauce has a silky mouthfeel. This is especially important when making a pan sauce that is based on deglazing and reduction.
Reduction alone can leave a sauce tasting a little one dimensional. Before a reduction sauce is truly done, a chef knows to swirl in just a bit of heavy cream, cool butter or compound butter (butter kneaded together with other flavoring agents, such as fresh herbs, spices, citrus zest, etc) to create a more mellow and well-rounded flavor profile and to enrich a sauce for a more luxurious mouthfeel.
When finishing with butter or compound butter, it is called mounting. Always mount butter off the heat into a very warm but not steaming sauce.
Add a little bit of cool butter at a time while swirling the pan or whisking. What you are doing here is creating an emulsion, so adding the butter slowly will help keep it from separating.