Preheat the oven to 375°F (190°C). Butter a 9x13-inch baking dish.

Bring a large pot of salted water to a boil and cook the pasta until 1–2 minutes shy of al dente. Drain and reserve 1 cup pasta water.

Season the chicken with salt and pepper. Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add chicken and sear until golden and almost cooked through, about 4–5 minutes. Remove chicken to a plate.

Reduce heat to medium and add the remaining butter to the skillet. Add onion and cook until translucent, 3–4 minutes. Stir in garlic and cook 30 seconds.

Sprinkle flour over the onion mixture and cook, stirring, for 1–2 minutes to remove raw flour taste. Slowly whisk in milk (or milk + cream) until smooth. Bring to a low simmer; the sauce will thicken in 2–3 minutes.

Stir in cream cheese (if using) and half the Parmesan until smooth. Taste and adjust seasoning with salt, pepper, and thyme.

Return the chicken to the skillet and fold in the drained pasta. If the sauce seems too thick, add a splash of reserved pasta water to loosen.

Transfer everything to the prepared baking dish. Top with mozzarella, remaining Parmesan, and panko breadcrumbs (if using). Dot a little butter on top for extra browning.

Bake for 15–20 minutes until bubbly and golden. If you want a deeper crust, broil for 1–2 minutes while watching carefully.

Let rest for 5–10 minutes before serving to allow the sauce to set.