In a large Dutch oven, cook the squash (peeled and chopped) covered, in enough boiling salted water to cover for 25 to 30 minutes or until tender; drain. Return to pan. Alternatively, you can half the squash and roast it in the oven until tender. Then scoop out the flesh of the squash and place it into a large mixing bowl.
Preheat oven to 350°F. Grease a rectangular baking dish with butter or cooking spray. Set aside.
Mash squash with a potato masher or blend with a stick blender. Gradually temper about 1 cup of the mashed hot squash into the beaten eggs by adding it slowly with constant stirring (this will prevent your eggs from scrambling!). Add the mixture to the remaining squash in the pan.
Add butter, brown sugar, 1/4 cup maple syrup, and the milk. Whisk until well combined before transferring squash mixture to the prepared baking dish.
Bake, uncovered, for 25 minutes.
Cook bacon and onion over medium heat for about 10 minutes or until bacon is slightly crispy and onion is tender. Remove from heat, drain off any excess fat and stir in the cinnamon.
Top the casserole with the bacon and onion mixture. Bake, uncovered, for about 10 minutes more or until edges are set and casserole is heated through. Drizzle with additional maple syrup. Let stand for 10 minutes before serving.