Ecuadorans like to top a llapingacho with a fried egg for lunch and serve it with fish for dinner. The recipe below comes from A Passion for Potatoes by Lydie Marshall (HarperCollins, 1992).
4 medium russet potatoes
3 tbsp. butter
3 medium yellow onions, peeled and finely chopped
Salt and freshly ground black pepper
1/2 lb. queso blanco or muenster cheese, grated (about 2 cups)
4 tsp. olive oil
1. Put potatoes into a medium pot and cover with cold water by 2"–3". Bring to a boil over medium-high heat, reduce heat to medium, and gently boil until potatoes are tender when pierced with the tip of a knife, 20–30 minutes. Drain and allow to cool. Peel potatoes, grate on the large holes of a box grater into a large bowl, and set aside.
2. Melt butter in a medium pot over medium-low heat. Stir in onions, cover, and cook until soft, 30–35 minutes. Allow to cool. Mix onions into potatoes, add salt and pepper to taste, and divide into 12 balls. Make a well in each potato ball and bury 3 tbsp. of the cheese in center of each. Flatten balls into 3 1/2"-wide cakes, then refrigerate for 30 minutes.
3. Heat oil in a nonstick skillet over medium heat. Working in batches, fry cakes until browned on each side, about 4 minutes per side.