Warm corned beef in a small bowl in microwave on High, 30 seconds to 1 minute.
Heat a skillet over medium heat.
Place 1 tortilla in the hot skillet.
Sprinkle with Monterey Jack cheese, corned beef, and green chilies.
Top with the other tortilla.
Heat until bottom tortilla is golden brown, 2 to 4 minutes . Carefully flip and heat until other side is golden brown and cheese is melted, 2 to 4 minutes.