01 - Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
02 - Melt 3 tablespoons butter in a large skillet over medium heat. Add onions, carrots, and celery; sauté for 5 to 6 minutes until softened.
03 - Sprinkle flour over the vegetables and cook, stirring continuously, for 1 minute.
04 - Gradually whisk in the broth, followed by the milk. Cook while stirring until the sauce thickens, about 3 to 4 minutes.
05 - Stir in garlic powder, dried thyme, black pepper, and salt until well incorporated.
06 - Add cooked turkey and peas to the sauce mixture. Stir thoroughly and simmer for 2 minutes.
07 - Transfer the turkey and vegetable mixture evenly into the prepared baking dish.
08 - Sprinkle shredded cheddar cheese evenly over the turkey mixture.
09 - In a small bowl, mix breadcrumbs with melted butter; sprinkle uniformly over the cheese layer.
10 - Bake uncovered for 25 to 30 minutes until the topping is golden and bubbling.
11 - Optionally garnish with chopped fresh parsley. Serve hot.