Boil the potatoes in salted water until very tender, about 15 to 18 minutes. Drain thoroughly and let them steam dry.
Mash with the salt and cumin until mostly smooth. Let the mash cool enough to handle.
Shape and Fry:
Divide the mash into eight portions. Flatten each portion, place a cube of cheese in the center, and pinch the potato around it. Gently flatten into thick patties.
Heat the annatto oil in a large nonstick skillet over medium heat. Fry the patties for 4 to 5 minutes per side until golden and the cheese is melted.
Transfer to a warm plate while you finish the batch.
Make the Sauce and Serve:
Cook the onion in a small saucepan with a teaspoon of oil until soft. Stir in the peanut butter, milk, cumin, and salt.
Simmer gently for 3 to 4 minutes, whisking until smooth. Add a splash more milk if needed.
Serve the llapingachos with peanut sauce, fried eggs, avocado, curtido, and tomato salad.
Notes
Dry mashed potatoes make patties that hold together better.
Use a mild melting cheese if queso fresco is unavailable.
Keep the sauce warm over low heat and whisk before serving.