Preheat and prep: Heat the oven to 375°F (190°C).
Lightly grease a 9x13-inch baking dish. Bring a large pot of salted water to a boil for the pasta.
Cook the pasta: Boil the pasta until just shy of al dente (about 1–2 minutes less than package directions). Drain and set aside.
Toss with a teaspoon of olive oil to prevent sticking.
Season the chicken: Pat dry and cut into bite-size pieces. Season with 1 teaspoon salt, 1/2 teaspoon black pepper, and the Italian seasoning.
Sear the chicken: Heat 1 tablespoon olive oil in a large skillet over medium-high. Cook the chicken in a single layer until lightly browned and cooked through, 5–7 minutes.
Transfer to a plate and keep warm.
Start the sauce: In the same skillet, reduce heat to medium. Add butter and remaining 1 tablespoon olive oil. Stir in minced garlic and cook 30–60 seconds until fragrant.
Make a light roux: Sprinkle in the flour and whisk for 1 minute to cook it out.
Slowly whisk in the chicken broth, then the milk, until smooth.
Thicken and enrich: Simmer 2–3 minutes, stirring, until slightly thickened. Remove from heat. Whisk in the Greek yogurt until fully incorporated and silky.
Add the cheeses: Stir in 3/4 cup parmesan and 1 cup mozzarella until melted and smooth.
Add a pinch of red pepper flakes if using. Taste and adjust salt and pepper.
Combine: Add the cooked chicken and pasta to the skillet, folding gently to coat everything in sauce.
Assemble the bake: Transfer to the prepared baking dish. Top with remaining mozzarella and parmesan.
If using, mix panko with a teaspoon of olive oil and sprinkle over the top for crunch.
Bake: Bake 15–20 minutes until bubbling at the edges and the top is lightly golden. For extra color, broil for 1–2 minutes, watching closely.
Finish and serve: Rest 5 minutes to set. Garnish with chopped parsley.
Serve warm.