Prepare spaghetti according to package directions; drain. In a large pot, cook broccoli in boiling water until crisp yet tender, about 4 minutes. Drain and add to pasta. Add onions, garlic, peas, bell peppers, mushrooms, and parsley to pasta. To prepare dressing, combine vinegar, lemon juice, mustard, oil, salt, basil, oregano, thyme, black pepper, and cayenne pepper in a mixing bowl. Pour dressing over pasta mixture and toss gently until well mixed.