Turkey Noodle Casserole

Preheat oven to 350°F. Bring a large pot of water to a boil over high. Add noodles; cook according to package directions, adding broccoli during final 3 minutes cook time. Drain; rinse under cold water, and drain again. Set aside.

Melt butter in a large saucepan over medium-high until foamy. Add onion, carrot, celery, garlic, and thyme; cook, stirring occasionally, until softened, 4 to 5 minutes. Whisk together flour and 1/2 cup of the milk in a bowl until smooth. Add remaining 3 1/2 cups milk to onion mixture; bring just to a boil over medium-high, whisking constantly. Whisk in flour mixture, salt, and pepper. Reduce heat to medium; simmer, whisking occasionally, until sauce is slightly thickened, about 3 minutes.

Stir together noodle mixture, sauce mixture, and turkey in a large heatproof bowl until combined. Spoon mixture into a 13- x 9-inch baking dish coated with cooking spray. Sprinkle evenly with cheese. Bake in preheated oven until cheese is bubbly, 25 to 30 minutes. Let stand 5 minutes. Serve.