Spread mustard on 1 side of each. Divide corned beef among bread slices. Top with cheese and onion. Cover with remaining 4 bread slices, pressing slightly to adhere.
Melt 2 tablespoons butter in each of 2 large nonstick skillets over medium heat. Place 2 sandwiches on each skillet and cook until golden brown on bottom, pressing occasionally with spatula, about 3 minutes. Turn sandwiches over and cook until golden on bottom and cheese melts, about 3 minutes. Transfer sandwiches to plates, cut in half and serve.