Quarter potatoes and boil in salted water until the outsides begin to crumble, about 25 minutes.
Drain and mash until smooth.
Mix onion and parsley with crumbled cheese.
Grab a handful of mashed potato and form into a bowl in your palm.
Place a tablespoon of cheese mixture into a bowl. Seal the potato around the cheese forming a pancake about 1 inch thick and 3 inches wide. Repeat with remaining potatoes.
Fry each side until brown and crispy in a lightly oiled skillet.
Shred lettuce. Serve two llapaingachos on shredded lettuce with peanut sauce.