Add the whole potatoes to a large pot of water and boil for 25 minutes.
Put the ice in a large bowl and cover with cold water. Drain the potatoes and add them to the ice bowl. Let them sit and cool for 5 minutes, then drain.
Cut the potatoes in half. Using a melon baller, scoop out some potato in each half, positioning it off center to resemble an egg. Put the potato that you scoop out in a medium bowl.
Mash the potato chunks that you put into the bowl, then add the mustard, mayonnaise, vinegar, salt, turmeric, and pepper. Stir and mash until the mixture is very smooth.
Put the filling in a piping bag with a tip or a Ziploc baggie with the end snipped off. Fill each potato hole with the egg mixture.
Sprinkle the vegan deviled eggs with the smoked paprika and fresh dill, then serve.