Taste a piece of peel. If it is bitter, peel fruit with a vegetable peeler or slice fruit in half and scoop flesh directly into the bowl of a food processor. If it is not bitter, cut out leaves and cap and slice in quarters, then add to food processor. Add sugar, water and ginger and process until smooth. Set aside.
Line a baking sheet with nonstick foil. In a small saucepan, melt honey, butter and ginger over medium heat. Stir in walnuts and cook about 5 minutes, until some of the liquid begins to evaporate. Pour nuts onto foil-lined sheet; spread out slightly to cool.
Serve sauce and Honey Walnuts over vanilla ice cream or frozen yogurt. Makes about 1-1/2 cups sauce.