Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain.

Heat half-and-half in the microwave until just warm.

Process unpeeled potatoes through a food mill into a medium bowl. (Or, using a potholder, peel and drop them into a bowl. Puree using a potato masher or stand mixer fitted with the paddle attachment.) Stir in warm half-and-half and salt (or beat, if using a mixer) until smooth and fluffy. Cool, cover, and refrigerate potatoes in a microwave-safe, airtight container for up to 2 days.