In a blender or food processor, combine half and half, peanut butter, honey, and sugar. Blend until very smooth, about 30 seconds. Blend in salt ¼ teaspoon at a time to taste. Move blender carafe to refrigerator and chill until mixture is very cold, about 3 hours.
Churn chilled base in ice cream maker according to manufacturer's instructions. Transfer to freezer to firm for 3 to 4 hours before serving.
