Cook the tortellini: Bring a large pot of salted water to a boil. Cook the tortellini according to package directions until just tender. Reserve 1/2 cup pasta water, drain, and set aside.
Season and sear the chicken: Pat chicken dry, then season with salt, pepper, and half the Italian seasoning.
Heat 1 tablespoon olive oil in a large skillet over medium-high. Sear chicken in a single layer, 4–6 minutes total, until cooked through with golden edges. Transfer to a plate and tent loosely with foil.
Build the roux: Lower heat to medium.
In the same skillet, add butter. Once melted, stir in minced garlic and cook 30 seconds until fragrant. Sprinkle in flour and whisk for 1 minute to form a smooth paste.
Whisk in liquids: Slowly stream in chicken broth while whisking to avoid lumps.
Add milk and cream, whisking until smooth. Simmer 2–3 minutes until slightly thickened.
Add flavor and protein: Reduce heat to low. Stir in Parmesan, remaining Italian seasoning, and a small pinch of red pepper flakes if using.
Taste and adjust salt and pepper. Remove pan from heat and whisk in the Greek yogurt until the sauce turns silky. Return to low heat if needed, but don’t let it boil after adding yogurt.
Add chicken and greens: Stir the cooked chicken and any juices back into the skillet.
If using spinach, fold it in and cook 1–2 minutes until just wilted.
Toss with tortellini: Add tortellini to the sauce, tossing gently to coat. If the sauce feels too thick, splash in a little reserved pasta water until glossy and creamy.
Finish and serve: Top with extra Parmesan and chopped parsley. Serve hot with black pepper to taste.