Melt butter in a medium saucepan over medium heat. Cook sweet potatoes, stirring, until tender, 10 to 15 minutes; season with salt. Add half-and-half; cover. Let simmer for 10 minutes.
Transfer sweet potatoes and liquid to the jar of a blender; blend until smooth. Strain mixture and use immediately or cool completely in an ice-water bath. Transfer to an airtight container and keep refrigerated until ready to use.