Preheat oven to 475°.
Combine first 4 ingredients in a small saucepan; bring to a boil. Combine water and cornstarch in a small bowl, stirring with a whisk. Add to juice mixture in pan, stirring with a whisk. Cook 2 minutes or until thick and glossy, stirring constantly.
Place hen halves, meaty sides up, on a foil-lined jelly roll pan coated with cooking spray; sprinkle hen halves with salt and ground ginger. Spoon juice mixture evenly over hen halves.
Insert a meat thermometer into meaty part of a thigh, making sure not to touch bone. Bake at 475° for 25 minutes or until the thermometer registers 180°.