Roast the spaghetti squash: Preheat your oven to 400°F (200°C). Halve the spaghetti squash lengthwise and scoop out the seeds.
Rub the cut sides with 1 tablespoon olive oil and a pinch of salt and pepper. Place cut-side down on a parchment-lined sheet pan and roast 35–45 minutes, until the flesh is tender and strands shred easily with a fork.
Cook the chicken: While the squash roasts, heat 1 tablespoon olive oil in a large skillet over medium heat. Season the chicken with salt, pepper, and Italian seasoning.
Cook 5–7 minutes, stirring occasionally, until the pieces are cooked through and lightly browned. Transfer to a plate.
Sauté the garlic: In the same skillet, reduce heat to medium-low. If the pan is dry, add a drizzle more oil.
Add the minced garlic and cook 30–60 seconds, just until fragrant. Don’t let it brown.
Build the light Alfredo: Sprinkle the flour over the garlic and whisk for 30 seconds to form a paste. Slowly whisk in the chicken broth, then the milk, stirring constantly to prevent lumps.
Bring to a gentle simmer and cook 3–5 minutes, until slightly thickened.
Add the cheeses and seasoning: Stir in the Parmesan and Neufchâtel (if using) until smooth. Add nutmeg and a pinch of red pepper flakes if you like a little heat. Taste and adjust salt and pepper.
The sauce should be silky and lightly coats a spoon.
Combine with chicken: Return the cooked chicken and any juices to the skillet, stirring to coat in the sauce. Keep warm over low heat.
Shred the squash: When the squash is cool enough to handle, use a fork to scrape the flesh into long strands. Pat lightly with paper towels if it seems watery.
Bring it all together: Add the squash strands to the skillet and gently toss until everything is well coated.
If the mixture looks too thick, splash in a bit more broth or milk. If it’s thin, simmer a minute to reduce.
Finish and serve: Sprinkle with extra Parmesan, chopped parsley, and a touch of lemon zest or juice to brighten. Serve hot straight from the skillet or pile it back into the squash shells for a fun presentation.