Place the potatoes in a large pot with enough cold water to cover generously and a large pinch of salt. Bring to a boil, then lower the heat slightly to prevent boiling over, and partially cover. Cook until tender (35 to 40 min. for medium potatoes, or 45 to 55 min. for larger ones). Drain and let cool to room temperature.
Peel and finely chop the hard-boiled eggs in a large bowl. Mash them slightly with a fork. Stir in the remaining ingredients. Cover and chill until needed.
Peel the potatoes, cut into chunks, and put in a large bowl. Smash the potatoes with a fork or a potato masher to a texture somewhere between mashed and chunky. Pour the dressing over the potatoes and stir until evenly combined. Cover and chill for several hours (or overnight).
Notes
*If you are preparing this salad as GLUTEN-FREE, just be sure to use brands of mayonnaise and mustard that are known to be GF.