Prepare the Filling: In a large skillet, melt butter over medium heat. Add onion, garlic, carrots, and peas, cooking until softened. Sprinkle in flour and cook for 1 minute to form a roux. Gradually whisk in chicken broth and milk, stirring until the sauce thickens. Season with salt and pepper, then stir in the chicken.
Assemble the Pie: Pour the filling into a pie dish. Cover with the top crust, crimp the edges to seal, and cut small slits in the top for steam to escape.
Bake: Preheat oven to 400°F (200°C) and bake for 30–35 minutes, until the crust is golden brown and the filling is bubbly.
Serve: Let cool slightly before slicing.
