In a large pot, cook linguini according to package directions in salted water. Reserve 1 cup of pasta water before draining. Place rhubarb in colander. Drain pasta over rhubarb. Wipe pot dry.
In the same pot, cook garlic in hot oil over medium heat for 30 seconds or until lightly golden. Add the pasta mixture. Remove from heat. Add the 6 ounces cheese and pasta water; toss to coat. Return to medium heat. Cook and stir until creamy, about 2 minutes. Add parsley and pepper; toss to combine. Sprinkle with additional Parmesan. Serve immediately.