Boil the potatoes: Place whole potatoes in a large pot, cover with cold water, an inch above the level of the potatoes.
Add salt (1 1/2 teaspoons for every quart of water used).
Bring to a simmer on high heat, then reduce heat to maintain a simmer.
Cook for 10 to 15 (or more, depending on the size of the potatoes), until pierced easily with the tines of a fork or a sharp knife.
Check frequently for doneness.
Once done, drain and place potatoes on a sheet pan to cool.
Let cool to room temperature or slightly warm. (You can speed up cooling by placing in the refrigerator if you have space.)
Blanch the green beans: While the potatoes are cooking, bring another pot of salted water to a rolling boil (2 quarts of water, 1 Tbsp salt).
Add the green beans.
Blanch for 4 to 5, more or less depending on the age and toughness of the beans.
Once cooked until tender, drain and place in a bowl of ice water to shock and stop the cooking.
Make vinaigrette: While the potatoes and green beans are cooking, make the vinaigrette.
Whisk together in a bowl the mustard, vinegar, tarragon, salt, and olive oil.
Cut potatoes into bite-sized pieces: Once the potatoes have cooled, cut them into 3/4-inch to 1-inch bite-sized pieces.
Place in a large bowl.
Toss with green beans, bell peppers, red onion, olives, vinaigrette to marinate: To the bowl add the green beans, strips of roasted peppers, red onion, and olives.
Toss with the vinaigrette.
Let marinate until ready to serve.
Toss with parsley, arugula: Once ready to serve, toss with the parsley and arugula.
