Rinse and pat dry arugula. In food processor, process arugula, walnuts, garlic, lemon juice, salt and pepper to taste. With the motor running, slowly drizzle in the olive oil. Taste and adjust seasoning if necessary. Set aside.
Scrub potatoes under cold running water. Cut in half lengthwise. Place in stockpot with 1 teaspoon salt and enough cold water to cover. Bring to a boil, reduce heat and simmer until the potatoes are tender, about 12 minutes. Drain and set aside.
Add more olive oil to the arugula mixture if it is too thick. While potatoes are still warm, toss with the arugula mixture.
Nutritional Analysis per serving: 402 calories, 6 g protein, 26 g fat, (59 calories from fat), 38 g carbohydrates, 0 mg cholesterol, 4 g fiber, 12 mg sodium