Peel the potatoes and finely grate. Squeeze out as much excess moisture as possible using a towel or your hands and transfer to a large bowl.
Grate the onion and add to the bowl of potatoes.
Toss the potato and onion mixture with the salt, nutmeg, pepper, eggs, and flour to form a thick mixture.
Add a 1/4 inch (6 millimeter) layer of vegetable oil to a large frying pan and place over medium low heat.
Once the oil is thoroughly heated, scoop out 1/3 cup (80 milliliters) of the potato mixture, form into a thin patty, and add to the pan. Repeat with one or two more potato pancakes depending on the size of your pan and without overcrowding.
Fry the pancakes until golden brown, about 2 minutes, then gently flip to cook the other side until golden.
Transfer the golden Kartoffelpuffer briefly to a towel-lined plate to soak any excess oil and repeat with the remaining batter.
Serve the Kartoffelpuffer while still warm with apple sauce, Kräuterquark, or Knoblauchsauce.
For a more sweet option, sprinkle the Kartoffelpuffer with sugar or cinnamon sugar. For a more savory option, add a sprinkle of chopped fresh herbs.