Peel the potatoes and boil them until they’re fork-tender.
Drain and mash the potatoes until very smooth. Mix in the achiote oil (or regular oil mixed with ground annatto or paprika), followed by the salt and cornstarch. Stir well to combine.
Lightly oil your hands to prevent sticking. Scoop some of the potato mixture into your palms and form a ball. Press a small well into the center with your thumb, fill it with shredded cheese, and then close the ball to seal the cheese inside. Gently flatten into a patty shape. This is the trickiest part, and it doesn’t have to be perfect!
Repeat with the remaining mixture, placing finished patties on a plate. If stacking them, separate layers with parchment paper to prevent sticking. Chill in the refrigerator for at least 30 minutes to help them firm up.
When ready to cook, preheat a griddle or skillet over medium heat with a light coating of oil. Avoid using too much oil, as excess moisture can make the patties fragile.
Sear the patties for about 10 minutes on the first side, or until golden and crisp on the bottom. Carefully flip and cook the other side. Try to flip only once—these patties are delicate and can break apart with too much handling.
Serve warm with rice, a fried egg, avocado, and a spoonful of tomate de árbol ají. Enjoy!