Purée 1 cup arugula, 1/2 cup spinach, basil, garlic, and walnut pieces in food processor until smooth. Add remaining arugula and spinach, and pulse until smooth. With machine running, pour in lemon juice and oil, and blend until combined. Season with salt and pepper, if desired.
To make Potato Salad:
Cook potatoes in large pot of boiling salted water 10 minutes. Add green beans, and cook 5 minutes more. Drain, and transfer to bowl. Cover to keep warm.
Heat oil in skillet over medium heat. Sauté fennel and shallot in oil 10 minutes, or until browned. Add sun-dried tomatoes and red pepper flakes, and sauté 3 to 4 minutes more.
Toss Pesto and fennel mixture with potatoes and green beans. Garnish with tomatoes, and serve.