Preheat oven to 400*.
Toss cubed squash in cooking oil and roast for about 40 minutes, until it begins to brown and is fork tender.
Turn oven heat down to 350*.
Meanwhile, heat oil in a skillet and sauté mushrooms until they begin to brown.
Add sage and garlic and cook for 2 minutes.
Add kale and cook until kale is wilted down.
Toss bread, squash and cooked mushrooms and kale together into a 2 quart casserole dish.
Pour broth over top.
Cover with a lid or foil and bake for 30 minutes.
After 30 minutes, add Parmesan cheese and bake for 10-15 more minutes or until top is crispy.