Put the whole potatoes, unpeeled into a large pot of salted water and bring to a boil. Cook until fork tender, about 30 mins. Do not let the skins split
Make the dressing while the potatoes are boiling
Mix the mayonnaise, mustard, chopped onion, chopped celery, chopped dill pickle, Lawrey's, and celery seed in a large bowl. Set aside in the fridge until the potatoes are cooked through.
When the potatoes are fork tender, remove them from from the pot and begin peeling them. If they're cooked well, the skins will just slip off and you can peel them by hand.
A small paring knife can loosen any stuck skin or cut out small brown spots or eyes.
Roughly chop the potatoes into bite sized pieces. Don't be precious about the shape, just make them bite sized.
Mix the still hot potatoes into the cold dressing. I find it easiest to mix with my hand (washed and/or gloved, of course). Don't overmix.
Chill the potato salad for a minimum of 4 hours but better overnight to let the flavors blend.