Cut the squash in half lengthwise; remove and discard seeds. Place squash on a baking sheet cut side down. Bake until tender, about 1 hour.
Separate the strands of squash with a fork and place in a medium bowl; discard shells. Squeeze out any excess liquid from the squash if watery.
Maintain the oven temperature.
Heat butter and oil in a large saucepan over medium heat. Add onions and cook about 2 minutes.
Stir in flour. Reduce heat to low and cook, stirring continually 3 – 4 minutes.
Add milk and chicken broth and continue whisking, raising heat to medium-high until it comes to a boil and becomes smooth and thick, about 2 minutes stirring; season with salt and pepper.
Once it becomes thick, remove from heat, add cheddar cheese and mix well until cheese is melted.
Adjust salt and pepper to taste, add cooked spaghetti squash and baby spinach, pour into a baking dish and sprinkle parmesan cheese on top.