Preheat oven to 375°F (190°C). Grease a 9×13-inch baking dish.

Cook penne pasta until al dente. Drain and set aside.

In a large skillet, melt butter over medium heat. Add onion, carrots, and celery. Cook for 5–7 minutes until softened.

Add garlic and cook for 1 minute more.

Sprinkle flour over the veggies and stir well. Cook for 1–2 minutes to remove raw flour taste.

Gradually whisk in chicken broth and milk, stirring until smooth. Simmer until the sauce thickens.

Stir in shredded chicken, frozen peas, thyme, salt, and pepper. Simmer for 2–3 more minutes.

Fold in the cooked pasta until evenly combined.

Pour mixture into the prepared baking dish.

Place puff pastry over the top, trimming and tucking edges as needed.

Brush the puff pastry with beaten egg.

Bake for 25–30 minutes, or until the crust is golden brown and the filling is bubbling.

Let cool for 5–10 minutes before serving.