Preheat the oven to 425°F.
Cut the spaghetti squash in half lengthwise and remove the seeds. Lightly mist both sides of the squash with cooking spray and sprinkle the flesh with salt and pepper. Place the cut sides down on the baking sheet. Cook for 30 to 45 minutes, or until the flesh is tender when poked with a fork. Cooking time will vary depending on the size of your squash. Allow the squash to cool on the baking sheet.
While the spaghetti squash is roasting, add the chicken breast, chicken broth, and salt and pepper to the pressure cooker. Seal the lid and cook on high pressure for 30 minutes. Depressurize and transfer the chicken breast to a cutting board. Shred the chicken with a fork or meat claws. Cover with foil to keep warm until you are ready to add it to the spaghetti squash.
As the squash cools on the baking sheet, heat the olive oil in a large frying pan and add the broccoli florets. Sprinkle with salt and pepper and toss to coat. Cook 3 to 4 minutes, or until tender. Remove the broccoli from the frying pan and transfer it to a large mixing bowl.
Melt the butter in the same frying pan. Add the onion and garlic and saute for 2 to 3 minutes, or until fragrant.
Whisk together the 2% milk and flour in a measuring cup and add it to the pan with the garlic. Add the evaporated milk. Whisk to incorporate. Bring the milk mixture to a simmer and cook for 4 to 5 minutes, or until thickened, whisking constantly to prevent burning. Remove the sauce from heat and stir in the grated Parmesan cheese, salt, and pepper.
Once the squash has cooled enough to handle, use a fork to carefully scrape out the flesh into the same bowl as the broccoli. Keep the squash boats for later. Add the shredded chicken. Pour about ⅔ of the Alfredo sauce over the squash mixture and mix well to combine.
Transfer the spaghetti squash mixture back to the squash boats and sprinkle with mozzarella cheese, if desired. Bake another 10 minutes. Finish on a high broil for 3 to 4 minutes, or until the cheese is golden brown. Remove and serve with reserved Alfredo sauce, if desired.