Grate the potatoes and onion finely or process them into a very fine mash in a food processor. Let the released excess liquid settle for 2 minutes, then carefully drain it off. (For extra crispy pancakes, squeeze the liquid out through a cloth).
Add the egg, flour, salt, and pepper to the potato-onion mixture. Mix well to combine the ingredients. The mixture should not be too runny, but not too thick either (it should slide easily off a spoon).
Heat the vegetable oil in a large frying pan over medium-high heat.
Spoon the mixture into the hot oil. Gently flatten it to form pancakes about 7-10 cm in diameter.
Fry for 3-4 minutes on each side until the Draniki are richly golden brown and crispy. After frying, transfer them to a plate lined with paper towel to remove excess fat.
Serve Draniki immediately while they are hot and crispy. Traditionally, they are served with a generous dollop of sour cream, optionally sprinkled with chopped dill. In some parts, they are served with a thick meat sauce (Machanka).