Cut potatoes into large chunks and boil in water until soft. Drain and allow to cool. Once cool, mash with oil, eggs, salt, pepper and dill.
Stir in potato starch until thoroughly combined, and refrigerate the mixture for 1 hour.
Bring soup or a pot of lightly salted water to a boil. Use your hands to gently form rough ball shapes from one tablespoon of batter at a time, and submerge dumplings in the soup or water - If you prefer, you may use a soup spoon or ice cream scoop to move free-form spoonfuls of batter into the pot. Boil for approximately 5-6 minutes - The dumplings will float up to the surface quickly but will need several additional minutes to cook all the way through.
Serve in soup, or as a side dish with butter or margarine and fried onions.