Preheat oven to 400˚F and line a large baking sheet with parchment or foil.
Using a shark kitchen knife, cut the spaghetti squash in half lengthwise. If difficult to cut, poke a few holes with a fork into the skin and microwave for 3-4 minutes to soften.
Using a large spoon, scoop out the seeds and scrape away some of the stringy flesh.
Lightly brush the inside of the squash with the oil and sprinkle with salt. Place cut side down on the baking sheet and transfer to the oven.
Bake the squash for 45 minutes to 1 hour or until the insides can easily be shredded with a fork.
Allow squash to cool for about 15 minutes, before scraping the flesh out with a fork, making sure to keep the skin intact. Place squash in a mixing bowl, lightly season with salt and pepper and set aside.
For the sauce:
In a large saucepan, melt the butter over medium heat. Add the broccoli and cook for 2-3 minutes until bright green and starting to soften.
Whisk in the cream and half and half. Turn the heat to low and heat to a simmer.
Remove from the heat. Whisk in the lemon juice and zest.
Stir in the cheese 1 cup at a time, stirring until smooth.
Stir in the spinach and nutmeg. Season with salt and pepper, to taste.
Add spaghetti squash to the skillet and toss with the alfredo sauce and broccoli. Adjust seasonings and fill the hollowed squash skins with the mixture.
Sprinkle each stuffed squash with the cheese and return to the oven. Broil for 2-3 minutes until golden brown and bubbling.
Top with chopped fresh basil and parmesan cheese. Serve immediately.