Peel potatoes and place in cold water. Using a box grater, grate potatoes and onions into large bowl.
Transfer potato-and-onion mixture to a colander set over a bowl, and squeeze out excess moisture. Return mixture to bowl. Starchy sediment can be added back to mixture, if desired.
In separate bowl, combine eggs, matzo meal or flour, fresh dill, if using, and salt and pepper, to taste. Combine all ingredients, adding more matzo meal if mixture is too wet.
In large skillet, heat 1/2-inch oil (or chicken fat) over medium-high heat. Drop tablespoon or serving spoon-size portions of mixture into hot oil, and press down with spoon to flatten. Fry until brown and crispy on edges; turn until golden brown on each side, cooking 3 minutes per side. Remove to paper towels to drain. Serve immediately with applesauce and sour cream.