Cook the spaghetti. Bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente. Reserve 1/2 cup of pasta water, then drain and set aside.
Season the chicken. Pat the chicken dry.
Season with 1/2 teaspoon salt and 1/2 teaspoon black pepper. You can add a pinch of garlic powder if you like.
Sear the chicken. Heat the olive oil in a large skillet over medium-high heat. Add the chicken and cook 4–6 minutes, stirring occasionally, until browned and cooked through.
Transfer to a plate.
Sauté the garlic. Reduce heat to medium. In the same skillet, add the minced garlic. Cook 30–60 seconds until fragrant, scraping up any browned bits.
Make a quick slurry. In a bowl, whisk the milk, chicken broth, and flour until smooth.
This helps the sauce thicken without lumps.
Build the sauce. Pour the slurry into the skillet with the garlic. Stir constantly until it begins to thicken, 3–5 minutes. Lower the heat to medium-low.
Add flavor and creaminess. Stir in the Parmesan, nutmeg, and red pepper flakes.
Once the cheese melts, remove the pan from heat. Whisk in the Greek yogurt and lemon juice until smooth. Return to low heat if needed, but do not boil or the yogurt may curdle.
Combine everything. Add the cooked spaghetti and chicken to the skillet.
Toss gently to coat. If using spinach, fold it in now and let it wilt. Adjust consistency with reserved pasta water, a splash at a time.
Finish and serve. Taste and adjust salt and pepper.
Plate, then top with extra Parmesan and chopped parsley. Serve warm.