1. Heat oil in large nonstick skillet over medium-high heat. Add onions and mushrooms; cover and cook 4 minutes. Uncover and cook, stirring frequently, 7 to 8 minutes or until lightly browned. Add beef, breaking up with spoon; cook until browned, 2 to 3 minutes more. Transfer to bowl.
2. Add eggplant and broth to same skillet; cover and cook 5 minutes. Uncover and add garlic, salt, thyme and red pepper; cook 2 minutes. Stir in vinegar. Reduce heat to medium; add tomatoes and beef mixture, breaking up tomatoes with spoon. Cover and simmer 5 minutes to blend flavors. Toss with hot pasta and parsley in large serving bowl.