Melt butter in a large nonstick skillet over medium-high heat; add turnips. Cook 10 minutes or until turnips are browned.
Add sugar; cook 30 seconds, stirring constantly. Add water and salt; stir well. Simmer, uncovered, 10 minutes or until most of the liquid is absorbed and turnips are tender. Transfer turnips to a large serving bowl; sprinkle with parsley, and toss gently.