1. Melt butter with oil in large skillet over medium heat. Add onions and cook, stirring occasionally, 5 minutes. Reduce heat to medium-low; cover and cook onions 20 to 25 minutes, stirring frequently, until golden.
2. Meanwhile, start to cook pasta according to package directions.
3. Uncover skillet. Add garlic to onions; increase heat to medium and cook 5 minutes. Add sun-dried tomatoes, half the parsley, salt, and red pepper flakes; cook 3 to 5 minutes more, until onion mixture thickens slightly.
4. Drain pasta. Reserve 1/2 cup pasta water. Transfer pasta to large bowl. Add pasta water and remaining parsley to onion mixture. Cook 2 minutes. Stir sauce into hot pasta and toss. Divide pasta among 4 serving bowls. Garnish with parsley sprigs, if desired. Makes 4 servings.