Separate cloves of garlic and drop into boiling water for 1 minute. Drain and peel. Place peeled cloves in small saucepan with oil and optional rosemary sprigs. Cook gently, covered, stirring occasionally, for about 25 minutes or until garlic is tender. Discard rosemary sprigs and puree garlic with 1/2 cup of the olive oil, basil, and the rosemary leaves.
Place pasta in large bowl and add garlic puree, chicken, onion, Parmesan, salt and pepper. Mix thoroughly. Add more olive oil if needed to moisten salad.
Let salad sit for 1 hour a room temperature (provided its not a hot room that will invite bacteria to go nuts!) or refrigerate, returning mixture to room temperature before serving. Toast walnuts in 375-degree oven for 10 minutes. Stir into the salad and serve over a mix of crisp, chilled lettuces.