Preparation Heat heavy small skillet over medium heat. Add whole black peppercorns; toast until fragrant and beginning to smoke, stirring often, about 3 minutes. Transfer to small bowl to cool. Coarsely crush peppercorns in mortar with pestle, or place peppercorns in resealable plastic freezer bag, and seal; crush with mallet. Transfer crushed peppercorns to small saucepan. Add 1 cup water, sugar, and scant 1/4 teaspoon salt. Bring to boil, stirring until sugar dissolves. Boil mixture until reduced to 1 cup, about 4 minutes. Refrigerate until cold. DO AHEAD: Black pepper syrup can be made 1 day ahead. Cover and keep refrigerated. Scoop persimmon flesh from skins into blender. Puree until smooth. Measure 2 cups puree for making ice cream, reserving any remaining puree for another use. Cover and chill puree until cold, about 2 hours. Strain black pepper syrup into large bowl. Whisk in 2 cups persimmon puree and cream. Process in ice cream maker according to manufacturer's instructions. Transfer ice cream to container, cover, and freeze. DO AHEAD: Can be made 1 day ahead. Keep frozen.
Preparation Heat heavy small skillet over medium heat. Add whole black peppercorns; toast until fragrant and beginning to smoke, stirring often, about 3 minutes. Transfer to small bowl to cool. Coarsely crush peppercorns in mortar with pestle, or place peppercorns in resealable plastic freezer bag, and seal; crush with mallet. Transfer crushed peppercorns to small saucepan. Add 1 cup water, sugar, and scant 1/4 teaspoon salt. Bring to boil, stirring until sugar dissolves. Boil mixture until reduced to 1 cup, about 4 minutes. Refrigerate until cold. DO AHEAD: Black pepper syrup can be made 1 day ahead. Cover and keep refrigerated. Scoop persimmon flesh from skins into blender. Puree until smooth. Measure 2 cups puree for making ice cream, reserving any remaining puree for another use. Cover and chill puree until cold, about 2 hours. Strain black pepper syrup into large bowl. Whisk in 2 cups persimmon puree and cream. Process in ice cream maker according to manufacturer's instructions. Transfer ice cream to container, cover, and freeze. DO AHEAD: Can be made 1 day ahead. Keep frozen.