
Prepare the potatoes. Peel the potatoes, then boil in salted water. Drain the water, roughly chop the still-warm potatoes, and transfer them to a large bowl.
Mix the salad. Add the eggs, ham, onions, pickles, olives, and peppers to the bowl. Stir to combine, further breaking down some of the potato pieces.
Make the dressing. In a separate bowl, combine all of the dressing ingredients. Pour the dressing over the potato mixture and stir again to combine. The potatoes will break down even more, making the potato salad a mixture of creamy mashed potatoes and bite-sized potato chunks.
Cool and serve. Store covered in the refrigerator until ready to serve. If your potato salad is a little thick, feel free to stir in more mayonnaise before serving.