Preheat oven to 400°F (200°C).
Melt butter in a skillet over medium heat. Add onion and cook until softened. Stir in garlic and cook until fragrant.
Add carrots and cook for 2–3 minutes. Sprinkle flour over the vegetables and stir well.
Slowly pour in chicken broth and milk, stirring constantly until a smooth, creamy sauce forms.
Stir in chicken, peas, salt, pepper, and thyme. Remove from heat.
Transfer the filling to a baking dish. Place puff pastry over the top, trimming excess and cutting small slits for steam.
Brush the pastry with egg wash.
Bake for 30–35 minutes, or until the pastry is golden brown and the filling is bubbling.
Let rest for 5 minutes before serving.