Put your potatoes in a pot with enough water to cover by 1/2 an inch + 2 teaspoons salt + 1 Tablespoon vinegar. Start covered with medium high heat until the water starts boiling (15 to 20 minutes), then put the lid askew, turn the heat down to medium low, and cook another 20 minutes or so until you can pierce the center of the thickest piece with a skewer or fork like a warm knife through butter.

While the potatoes are going, hard boil your eggs. Some people like to put them in with the potatoes, but it's just easier for me to keep track of them in a separate pot. I usually start with cold water, bring the water up to a gentle boil and let the eggs continue cooking another 4 minutes or so for a hard boil. Once the eggs are boiled, drain the hot water and cover them with cold tap water. This stops the cooking process and keeps the yolks from getting that green ring.

Put your minced carrots, celery, and onion in a bowl and barely cover with pickle brine, add 1.5 teaspoons salt and stir to dissolve. I find small, controlled stirring action at the bottom of the bowl does a quicker job of dissolving the salt. Let the veg sit in the brine until it's time to mix the potato salad.

When potatoes are cooked through, take them out of the pot, drain well, and let them cool for at least 20 minutes or so before peeling. This is a good time to peel and chop your eggs into roughly 1/2-inch pieces and set aside.

Cut the potatoes into roughly 1-inch cubes, place in a mixing bowl, and toss with 1/3 cup pickle brine and 1 teaspoon salt sprinkled evenly over all the potatoes.

Squeeze the excess liquid out of the veg mixture in fistfuls and add it to the potatoes along with the minced pickles. (The reason for steeping the veg in the brine is to season it all the way through and, in squeezing the excess liquid, giving it a pickled crunch without adding extra liquid to your salad.)

Add 1 cup of mayonnaise and 2 Tablespoons of mustard to start and gently fold the potato salad mixture to season evenly. Give it a taste because the next step is where you're going to adjust your seasoning if you need to.

Add chopped eggs and adjust seasoning if needed - additional mayonnaise for more creaminess, mustard for more of that mustard punch, maybe a *little* more salt or pickle brine if you think the potato pieces could use a little more seasoning, black pepper to taste - and fold gently again to incorporate thoroughly.

Potato salad's done! Store in fridge until serving. Enjoy! :)