Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
Heat olive oil in a large saucepan over medium low heat. Saute onion and garlic until soft and translucent, about 5 minutes. Increase heat to medium high. Stir in mushrooms, and cook until lightly browned, about 5 minutes. Stir in the eggplant, and cook 5 minutes. Stir in the tomatoes, chicken broth and olives. Season with thyme, salt and red pepper flakes. Bring to a boil. Reduce heat, cover, and simmer 30 minutes, or until eggplant is tender. Toss with pasta and goat cheese.