Bring a large pot of salted water to a boil. Add potatoes and cook until tender but still firm, about 15 minutes. Drain and cool.
Mash potatoes and bread cubes together in a large bowl. Mix in egg, salt, cayenne, jalapeno, and cilantro. Shape potato mixture into patties and coat with bread crumbs.
Heat oil in a large tall-sided skillet until almost smoking. Carefully slide cutlets into oil. Cook, turning once, until golden brown on both sides. Remove from heat and drain. Serve warm.