Preheat oven to 350 degrees F.
Heat butter and olive oil in a large skillet set over medium-high heat. Add onions to the pan. Sauté onions until they are light golden, 5 to 8 minutes.
Add butternut squash to the onions and sauté for 4 minutes. Add sugar, ¾ teaspoons salt, ¾ teaspoon pepper, and nutmeg to the mixture. Stir well and sauté until the onions and squash begin to caramelize, 5 to 6 minutes.
Pour the vegetable mixture into a 13x9x2-inch glass baking dish that is coated with cooking spray. Spread the vegetables evenly in the dish and pour chicken broth over top. Cover tightly with foil and bake for 45 minutes.
Remove the dish from the oven. (The recipe can be prepared until this point 1 day ahead. Cool, then cover and refrigerate. Reheat in a 350 degree F oven for 10 minutes.)
Increase the oven temperature to 400 degrees F.
In a medium bowl, mix breadcrumbs, Parmesan cheese, sage, ½ teaspoon salt, and ½ teaspoon freshly ground black pepper. Sprinkle evenly over the squash mixture.
Bake, uncovered, until the top is golden brown, 15 to 20 minutes. Serve.