Rinse and scrub potatoes, cut into cubes, about 1-1/2 inches. Add potatoes and 1 tablespoon salt to a large pot, completely cover potatoes with water and bring to a boil. Reduce heat to a low-boil. Cook until potatoes are tender when pierced with a fork, 15-20 minutes. Drain potatoes, cover, and set aside.
Add remaining ingredients, except red onion, celery, and dill to the creamed cashews. Whisk until well combined. Note: mayo will thicken up after several hours, and is best when made the night before.
Add onions, celery, and dill to potatoes, toss to combine.
Plant-Based Mayonnaise
Add rinsed cashews, 3/4 cup water, and remaining ingredients to a high speed blender, pulse until a creamy consistency. Pour mixture into a bowl, cover and refrigerate until ready to use. Try making this the night before to allow the mayo time to thicken.
Pour about 1 cup mayo over the potatoes, toss to combine. Add additional mayo for the ultimate creamy potato salad. Lightly sprinkle the potato mixture with paprika.