In a small saucepan, cook chopped carrots, covered, in a small amount of boiling water for 6-8 minutes, or until tender; drain.
In a food processor, combine cooked carrots, beans, tahini, lemon juice, garlic, cumin and salt. Cover and process until smooth. Transfer to a small serving bowl. Stir in parsley.
Cover and chill for at least one hour. If necessary, stir in enough water, 1 tablespoon at a time, to reach dipping consistency. If desired, garnish with carrot and/or lemon peel. Serve with assorted dippers.