Heat the oven and prep the squash. Preheat to 400°F (200°C). Halve the spaghetti squash lengthwise and scoop out the seeds. Rub cut sides with 1 tablespoon olive oil and a big pinch of salt and pepper. Place cut side down on a parchment-lined sheet pan.

Roast until tender. Bake 30–40 minutes, depending on size, until the skin gives when pressed and strands pull away with a fork. Let cool slightly, then use a fork to shred into strands. Pat with paper towels if very moist.

Season and sear the chicken. While the squash roasts, toss chicken with salt, pepper, and Italian seasoning. Heat the remaining 1 tablespoon olive oil in a large skillet over medium-high. Sear chicken 5–7 minutes, stirring once or twice, until cooked through and golden. Transfer to a plate.

Make the garlic base. Lower heat to medium. Add butter to the same skillet. When melted, add garlic and cook 30–60 seconds until fragrant. Do not brown.

Add liquids. Pour in chicken broth and scrape any browned bits from the pan. Stir in heavy cream and bring to a gentle simmer.

Thicken with cheese. Reduce heat to low. Stir in Parmesan a handful at a time until smooth and slightly thickened, 2–3 minutes. Add red pepper flakes if using. Taste and adjust salt and pepper.

Finish the sauce. Add lemon juice if you want a little brightness. Return chicken and any juices to the skillet. Simmer 1–2 minutes to marry flavors.

Combine with the squash. Add spaghetti squash strands to the skillet and toss gently to coat. Warm through for 1–2 minutes. If the sauce seems too thick, splash in a bit more broth or cream. If too thin, simmer briefly.

Garnish and serve. Top with extra Parmesan and chopped parsley. Taste one last time and adjust seasoning. Serve hot.