Boil a large pot of salted water. Cook pasta until al dente. Reserve 1/2 cup water, then drain.
Heat olive oil in a wide skillet over medium-high heat. Brown the turkey, breaking it up, 5–6 minutes.
Season with salt and black pepper. Stir in onion, carrot, and celery. Cook until softened, 4–5 minutes.
Add garlic, red pepper flakes, and tomato paste. Cook until fragrant and darkened, 1–2 minutes.
Pour in Worcestershire and chicken broth. Scrape up browned bits and bring to a simmer.
Stir in crushed tomatoes, oregano, basil, and sugar. Simmer gently 10–12 minutes, stirring occasionally.
Finish the sauce with butter and half the parsley. Taste and adjust seasoning.
Add drained pasta to the pan. Toss, loosening with splashes of pasta water as needed.
Fold in half the Parmesan. Serve topped with remaining Parmesan and parsley.