Wrap the grated potatoes in a large clean towel and squeeze out the excess starch. Get them as dry as possible. Unwrap and put the potatoes in a large mixing bowl. Add 2 teaspoons of the salt, 1 teaspoon of the white pepper, and the olive oil and toss to mix well. Form the mixture into 12 small cakes about 3 inches in diameter and 1 inch thick.
Heat the vegetable oil in a 10 or 12 inch nonstick skillet over medium-high heat until it's hot but not smoking. Fry the cakes, several at a time, until they are golden brown and cooked through, about 4 minutes on each side. Drain on paper towels and keep warm.
Pour off the oil and wipe the skillet clean set aside.