Heat broth in a small saucepan. Remove from heat. Add tomatoes. Let stand until soft. Drain reserving broth. Slice tomatoes into thin strips.
Heat oil in a heavy large skillet over high heat. Add minced garlic; sauté until golden, about 1 minute. Add reserved broth, sun-dried tomatoes strips, mushrooms, zucchini, broccoli rabe florets and basil. Simmer until vegetables are tender, about 3 minutes. Cook linguine in a large pot of boiling salted water until tender but still firm. Drain linguine; return to pot. Add vegetables and toss to combine. Season with salt and pepper to taste.
Transfer pasta mixture to bowl; sprinkle with Parmesan cheese.