Peel turnips and dice into 1-inch chunks. Arrange turnips in a single layer in a large nonstick pan over medium heat. Pour in water, and scatter butter and brown sugar over the top. Cover, and let cook for about 10 minutes, stirring occasionally.
Remove lid and continue to cook until liquid is evaporated, stirring to keep turnips from sticking. Once liquid is evaporated, salt and pepper to taste, and sprinkle on herbs if using.