Cook pasta according to package directions and add broccoli during the last 3 minutes of cooking, then drain.
Heat olive oil in a large skillet over medium heat.
Add garlic and sauté until fragrant.
Stir in cooked chicken and heat through.
Pour in milk and bring to a gentle simmer.
Stir in Greek yogurt, Parmesan cheese, salt, pepper, and Italian seasoning.
Add cooked pasta and broccoli to the skillet and toss until evenly coated.
Simmer for 2–3 minutes until creamy and heated through.
Sprinkle red pepper flakes if desired and serve warm.