1. Prick the sweet potato in several places, place on a paper towl, and microwave until tender, 8 to 9 minutes, turning half-way through cooking time. Let stand until cool enough to handle, then slip off skin.
2. Put a large pot of water on to boil. Pre-heat broiler and spary, or lightly oil, a baking sheet. Cut potato crosswise into 1/2 inchslices andplace on prepared sheet.
3. In a small saucepan, combine sugar, oil, butter and water. Cook over medium heat, stirring constantly, until sauce is smooth and bubbly, about 2 minutes. Reserve about 2 tablespoons of sauce. Brush remaining sauce over potato slices, sprinkle with Parmesan cheese, and broil until slightly browned, 1 to 2 minutes.
4. Cook fettucine according to package directions, drain well, and toss with reserved sauce. Mound pasta on serving plates and top with potato slices.