Wash and scrub the potatoes. Chunk them so all pieces are the same size.
In a large mixing bowl, toss the potatoes with olive oil, garlic and rosemary. Transfer to a baking sheet and roast in the oven at 450 till crispy on the outside and tender (about 30 minutes). Remove from the oven.
While potatoes are roasting, whisk together the mustard, oregano and lemon juice and slowly whisk in the oil until completely incorporated. Season with salt and pepper to taste.
In the large bowl, combine the artichokes, roasted red peppers and parsley with the dressing. Let the flavors marinate for 30 minutes, mixing occasionally, then serve at room temp.