Arrange radishes in a large deep skillet and add enough water to cover. Add butter, oil, sugar and salt. Cover and bring to a boil. Reduce heat to medium-low and simmer covered until radishes are tender when pierced with a knife and liquid has been reduced to a glaze, about 12 min. (If radishes cook before liquid has reduced, remove them and continue to cook the liquid, uncovered, until it becomes a glaze.) Toss radishes in glaze and garnish with pepper and parsley.
Braising tenderizes radishes and mellows their peppery taste.