Clean the potatoes and boil them with the peel on. Boil them until the peel begins to crack, that's how you'll know they're done.
Drain the potatoes and set them aside to cool until you can handle them.
Hard boil the 18 eggs, and set them (unpeeled) in cold water until they're cool. This step can also be done in advance if you want to save some waiting time for them to cool.
Peel the potatoes, then chop them into bite size pieces (about 1 inch cubes). Place the chopped potato in a very large bowl.
Once the boiled eggs have cooled enough to peel, chop them into small pieces. Add the chopped pieces to the potatoes.
Chop the onion and the pickles into very small, minced pieces. Grandma always made us do this by hand, but you can do it with a food chopper if you're pressed for time.
Add the pickles and the onions to the potatoes and eggs.
Add in and mix the mayo, yellow mustard, and salt and then use a large spoon to mix until it's all incorporated.
Cover the potato salad and place it in the fridge for 24 hours, or overnight if you waited til last minute.
If the potato salad seems very dry the next day, it's because the potatoes absorbed some of the liquid. Add up to half a cup more of mayo to help re-moisten it, if needed.