Place the potatoes in a large pot, cover with salted water, and bring to a boil. Cook for about 10-12 minutes until the potatoes are tender but still firm in the center.
Drain the potatoes and rinse them under cold water to cool them down quickly.
In a large mixing bowl, combine the cooled potatoes with the coconut yogurt, lemon zest, lemon juice, and chopped parsley. Season with salt and pepper to your liking.
Mix everything together until the potatoes are well coated, then your creamy potato salad is ready to serve!