Brown the turkey: Heat 1 tablespoon olive oil in a large skillet over medium-high.
Add ground turkey, breaking it up with a spatula. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook until no longer pink and lightly browned, 5–7 minutes.
Transfer to a plate.
Sauté aromatics: In the same pan, add remaining olive oil and 2 tablespoons butter. Stir in onion and cook until soft, about 3 minutes. Add garlic and cook until fragrant, 30–60 seconds.
Add herbs and spice: Sprinkle in Italian seasoning and red pepper flakes.
Stir for 15 seconds to bloom the flavors.
Build the sauce: Pour in chicken broth and bring to a simmer, scraping up any browned bits. Stir in cream and remaining 1 tablespoon butter. Season with remaining salt and pepper.
Simmer 2–3 minutes to slightly thicken.
Cook the tortellini: Add tortellini directly to the skillet. Stir to coat and cover. Cook over medium, stirring once or twice, until tender, 4–6 minutes (check package timing).
If sauce thickens too quickly, add a splash of broth.
Finish with turkey and greens: Return browned turkey and any juices to the pan. Add spinach (if using) and cook until wilted, 1 minute.
Brighten and cheese it up: Take off the heat. Stir in Parmesan, lemon zest, and lemon juice.
Taste and adjust salt, pepper, and lemon. The sauce should be glossy and coat the pasta.
Serve: Top with fresh parsley or basil and extra Parmesan. Serve hot.