Add the potatoes in a large pot and cover with water. Bring to a boil, and continue to cook for 5 - 10 minutes until potatoes are fork tender. Drain and let cool. Rinsing with cool water will help the potatoes cool faster.
In a large bowl, mix together the mayonnaise, pickles, vinegar, mustard, celery seed, dill, salt, and pepper. Add the cooled potatoes along with the celery and red onion and gently toss to coat in the dressing. Sprinkle with paprika for garnish before serving. Serve the vegan potato salad fresh or cover and store in the fridge for 3 - 4 days.
Vegan Mayonnaise: for a lower fat or oil-free version, sub the mayonnaise for 1 cup plain non-dairy yogurt or 1 cup of my vegan sour cream recipe from Fuss-Free Vegan (page 207).Potato peels: I like to leave the potato peels on for convenience, texture, and colour, but if you prefer you are welcome to peel the potatoes first. Egg flavor: traditional potato salad often contains hard boiled eggs. While I don't miss this flavor in this vegan potato salad, if you would like to add it, simply sub some of the salt with black salt (also called kala namak) which has an eggy taste.