Preheat oven to 400°.
Arrange onions, cut sides up, in a single layer in a shallow 2-quart baking dish coated with cooking spray. Brush tops of onions with oil; sprinkle with pepper and salt. Bake at 400° for 40 minutes. Add broth and soy sauce; bake 1 hour, basting every 15 minutes. Sprinkle sage and cheese evenly over onions. Bake an additional 5 minutes or until cheese melts.