Cook the pasta: Bring a large pot of salted water to a boil. Cook pasta until just shy of al dente.
Reserve 1 cup of pasta water, then drain and set aside.
Brown the turkey: In a large deep skillet, heat olive oil over medium-high. Add ground turkey, breaking it up with a spatula. Season with salt and pepper.
Cook until no longer pink and lightly browned, about 5–7 minutes.
Sauté aromatics: Add diced onion to the skillet and cook until translucent, 3–4 minutes. Stir in garlic, Italian seasoning, and red pepper flakes. Cook 30–60 seconds, until fragrant.
Build the sauce base: Reduce heat to medium.
Add chicken broth and milk, stirring to combine. If you prefer a thicker sauce, whisk cornstarch with a splash of cold milk to make a slurry and stir it in now.
Add veggies: Stir in broccoli florets. Simmer gently for 3–5 minutes, until the broccoli is crisp-tender.
If using spinach, add it later when the sauce is nearly finished.
Stir in Parmesan: Lower the heat to medium-low. Add grated Parmesan a handful at a time, stirring until melted and smooth. Sprinkle in nutmeg.
Taste and adjust salt and pepper.
Finish with yogurt: Remove the pan from heat for a minute to cool slightly. Stir in Greek yogurt until the sauce turns silky. Return to low heat only if needed to warm gently—don’t let it boil or the yogurt may split.
Combine with pasta: Add cooked pasta to the skillet, tossing to coat.
If the sauce is too thick, use reserved pasta water a splash at a time to loosen. If using spinach, fold it in now so it wilts.
Brighten and serve: Squeeze in lemon juice and toss again. Plate with extra Parmesan and chopped parsley.
Serve hot.