Boil the potatoes: Add potatoes to a large pot and cover with cool water. Bring to boil on the stovetop, and continue to cook for 10 minutes, or until potatoes are fork tender.
Cool the potatoes: Drain the potatoes and rinse under cold water to stop the cooking process. Let cool for 10-15 minutes, until they reach room temperature.
Make the dressing: In a large bowl, whisk together vegan mayo, tahini, dijon, lemon juice, dill, celery seeds, garlic, salt, and black pepper until smooth and well combined.
Assemble: Add the cooled potatoes, chopped pickles, celery, and shallot to the bowl with the mayo dressing. Gently mix until everything is coated.
Chill & serve: Cover with plastic wrap and refrigerate for at least an hour before serving. (While you can technically enjoy it right away, chilling allows the salad to cool completely and gives the flavors time to meld!)