In medium mixing bowl, combine masarepa, water, cheese, milk and salt, mixing thoroughly. Let mixture stand five minutes.
Using wet hands, knead dough until smooth. Divide dough into 18 portions; with wet hands, roll dough into small balls.
Heat butter in large griddle, or non-stick skillet over medium-high heat. Place balls of dough on hot surface about 3½" apart. Using palm of hand, flatten balls to form disks 3" diameter x ¼" thick. Cook, flipping once, until crisp and golden brown on both sides, about 7 minutes per batch. Serve warm.