Add potatoes to pot of salted cold water. Bring to a boil, over high heat, cover and reduce heat to a simmer and cook for 20 minutes or until tender. Drain the potatoes and cut into large chunks. Place the potatoes in a large bowl.
Warm the olive oil in a skillet over medium-high heat. Add the whites of the green onions and sauté for 3-5 minutes. Reduce heat to medium low, and stir in the remaining onions, dill, parsley, mustard, lemon juice, salt and pepper and warm through, 2-3 minutes. Remove from heat and add in capers. Pour the dressing over the potatoes and stir to combine. Serve warm or room temperature.
Store in the refrigerator, covered, for up to three days. Warm the salad a bit before serving.