Remove all but 1 tablespoon of the bacon drippings in the skillet. Add the onion, butternut squash, and Brussels sprouts into the pan along with 1 tablespoon butter.
Transfer the mixture into a 6-quart baking dish that has been sprayed with cooking spray. Cover the baking dish and bake in a preheated oven for 50 minutes.
Remove the cover and sprinkle the Parmesan cheese over top. Return the casserole back into the oven (uncovered) for 5-10 minutes to melt the cheese.
*Note - To make this dish vegetarian, omit the bacon and replace the beef broth with vegetable broth.