01 - Preheat oven to 375°F and lightly grease a 9x13-inch baking dish.
02 - In a large skillet over medium heat, melt 3 tablespoons butter. Add onions, carrots, and celery; sauté for 5 to 6 minutes until softened.
03 - Sprinkle flour over the softened vegetables and cook, stirring continuously, for 1 minute.
04 - Slowly whisk in broth followed by milk, stirring constantly until sauce thickens, about 3 to 4 minutes.
05 - Incorporate garlic powder, dried thyme, black pepper, and salt into the sauce.
06 - Add turkey and peas to the sauce mixture; stir well and simmer for 2 minutes.
07 - Evenly spread the turkey mixture into the prepared baking dish.
08 - Sprinkle shredded cheddar cheese evenly over the turkey mixture.
09 - Mix breadcrumbs with melted butter and distribute evenly over the cheese layer.
10 - Bake uncovered in the preheated oven for 25 to 30 minutes, until the top is golden and sauce is bubbling.
11 - Optionally sprinkle chopped fresh parsley over the casserole. Serve while hot.