Combine first 3 ingredients in a small saucepan. Cook over medium heat, stirring constantly, until sugar dissolves. Place cabbage in a small bowl. Pour vinegar mixture over cabbage; let stand at least 30 minutes.
Spread dressing evenly over 2 bread slices. Arrange turkey evenly over dressing. Drain cabbage mixture, and spoon evenly over turkey; sprinkle with cheese.
Place sandwiches on a baking sheet, and broil 5 1/2 inches from heat (with electric oven door partially opened) 1 to 2 minutes or until cheese melts. Top with remaining bread slices. Serve immediately.