In a large saucepan place potatoes in enough salted water to cover. Bring to boiling; reduce heat. Simmer, covered, for 15 to 20 minutes or until potatoes are tender; drain.
In a large bowl mash potatoeswith a potato masher or electric mixer on low to medium speed until smooth. Fold in cheese, eggs, cilantro, salt, cumin, and cayenne pepper. Shape mixture into twelve 3-inch-diameter patties. If desired, cover and chill for up to 24 hours before frying.
In a large skillet heat 1 inch of vegetable oil to 375 degrees F. Add potato patties, three or four at a time, and fry about 2 minutes or until golden brown, turning once halfway through frying time. Drain on paper towels. Serve hot. If desired, top with salsa.