For parsley butter: Finely chop parsley, lemon peel, and garlic in processor. Add butter and process until well blended. Season parsley butter to taste with salt and pepper. (Can be prepared 3 days ahead. Cover and refrigerate. Bring to room temperature before using.)
For pasta: Cook pasta in large pot of boiling salted water until just tender but still firm to bite. Drain. Transfer pasta to large serving bowl. Add parsley butter (about 1/3 cup) to pasta; toss to coat. Season to taste with salt and pepper.
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