Heat the unsalted butter in a heavy-duty saucepan over very low heat, until it’s melted. Let simmer gently until the foam rises to the top of the melted butter. The butter may splatter a bit, so be careful.
Once the butter stops spluttering, and no more foam seems to be rising to the surface, remove from heat and skim off the foam with a spoon. (It can be saved and added to soups, bread doughs, polenta, pilaf, or a bowl of warm oatmeal.) Don’t worry about getting every last bit; you can remove the rest when straining it.
Line a mesh strainer with a few layers of cheesecloth or gauze, and set the strainer over a heatproof container.
Carefully pour the warm butter through the cheesecloth-lined strainer into the container, leaving behind any solids from the bottom of the pan.