Preheat oven to 400 degrees F. Grease a 13x9-inch baking pan. Carefully slice the acorn squashes into rings 1/2 inch thick. Cover bottom of pan with several squash rings, place onion slices over rings, and add rest of squash rings on top. Add broth and olive oil. Sprinkle with cheese and parsley. Cover and bake for 30 to 45 minutes; uncover for the last 10 minutes.