The key to successful Llapingachos is using starchy potatoes (like Russet) that cook down well to form a firm yet creamy dough that holds its shape.
Traditionally, Llapingachos are served with a peanut sauce (salsa de maní) and curtido (red onion salad).
Cut the peeled potatoes into medium-sized chunks and boil them in a large pot with salted water until they are very tender and almost falling apart (about 20–25 minutes).
Drain the potatoes and immediately mash them into the smoothest puree possible. If the mixture is too sticky, let it cool slightly, or mix in 1 Tbsp of flour (optional). Let the mixture cool to room temperature.
Heat the achiote oil (or vegetable oil with achiote powder) in a skillet. Add the diced onion and sauté until softened and they gain a yellow-orange color (about 5 minutes).
Add the sautéed onion mixture to the potato puree. Mix thoroughly and season with salt and pepper. The potato mixture must be firm enough to be shaped.
Take about 1/4 cup of the potato mixture and form it into a ball. Use your thumb to make a well in the center, into which you insert a piece of cheese (queso fresco).
Seal the potato mixture around the cheese and flatten it into a patty about 7–8 cm (3 inches) in diameter and 1.5 cm (1/2 inch) thick. Repeat with the entire mixture. If the patties stick, you can use a little flour (or wet hands).
Heat butter or oil in a large skillet over medium heat. Fry the patties in batches. Cook them for 3–5 minutes per side until they are golden brown and crispy and the cheese inside begins to melt.
Keep the cooked Llapingachos warm until you have finished frying all of them.
Serve the Llapingachos hot with selected sides: a fried egg, avocado slices, and Curtido salad (red onion and tomato salad). Don't forget the traditional Salsa de maní (peanut sauce) for an authentic flavor!