Step 1

Simmer lima beans in water with 1teaspoon salt in a 5-quart pot, covered, until just tender, about 15 minutes.

Step 2

Purée beans with cooking liquid in batches in a food processor until smooth, then force purée through a medium-mesh sieve or a food mill fitted with fine disk into a large bowl.

Step 3

Heat half-and-half and butter in a small saucepan over moderate heat until butter is melted, then stir into bean purée along with cayenne, black pepper, and remaining 3/4 teaspoon salt. If purée is too thick, thin to desired consistency with additional half-and-half.