In a large pot over high heat, bring 8 cups of water to a boil. Add the potatoes and reduce the heat to a simmer. Boil the potatoes for about 20 minutes or until fork tender but not mushy.
Drain the potatoes in a colander and let cool for 5-10 minutes. When cool enough to handle, peel off the potato skins and cut the potatoes into ½-inch cubes. Place the potatoes in a large bowl.
Whisk the vegan mayonnaise, shallots, dill, vinegar, mustard, and salt in a small bowl until smooth and creamy.
Pour the dressing over the potatoes and stir gently to coat. Taste for seasoning and add more salt to taste if desired.
Place the potato salad in the refrigerator and marinate for at least 2 hours and up to overnight before serving
