Heat oven to 400°F. Slice a small pieceoff the skin side of each squash half, sohalves sit flat. Microwave on high in acovered bowl until flesh begins to soften,2 minutes. Gently simmer ginger, vinegarand sugar in a small saucepan over medium-low heat until liquid decreasesby 1/3, 8 to 10 minutes.
Remove from heatand set aside. Line 2 large baking sheetswith foil and coat with cooking spray.
Placesquash halves skin side down on bakingsheets. Arrange apple slices in cavity ofeach half.
Bake until apples soften, 25minutes.
Remove squash from oven,drizzle with balsamic sauce, return tooven and bake until apples brown, 5 to 6minutes.
Cut each squash half into quartersand transfer to a serving platter withany extra juices.