Place potatoes in large saucepan and cover with water. Bring to a boil; reduce heat to low and simmer for 15 minutes, or until easily pierced with fork. Drain and cool.
Transfer potatoes to a large bowl. Add pesto, tomatoes, artichoke hearts, pine nuts, salt and pepper (the pesto is so flavorful, you probably only need pepper, not salt). Gently stir together, carefully not to break potatoes. Cover and refrigerate for at least two hours.
Remove potato salad from refrigerator; stir in arugula prior to serving, if using.
Craving more veg-friendly recipes? Shop our collection of vegetarian and vegan cookbooks, including our new Vegan Thanksgiving and Vegan Christmas cookbooks!