Pour enough peanut oil into a skillet to cover the entire bottom.
Heat the oil and check if it is hot enough by dropping a small piece of grated potato into the oil – if it starts to fry, the temperature is good.
Place half of the potato mixture in the pan to form 2 Gromperekichelcher, flatten them and fry on each side for about 2-3 minutes.
Remove from pan and drain on paper towel.
Repeat with the remaining dough and make 2 more potato pancakes.
Fry on one side for 2 minutes, flip and cover the fried sides with ¼ grated cheese, half a slice of ham and the remaining cheese, then cover with the Gromperekichelcher that have already been fried.