Preheat oven to 375°F (190°C) and grease a 9x13-inch baking dish.
Cook egg noodles until just shy of al dente; drain and set aside.
Sauté onion, celery, and carrots in butter until softened.
Add garlic and cook 30 seconds.
Stir in flour and cook 1 minute.
Whisk in broth and milk until smooth.
Add cream of chicken soup, thyme, and parsley; simmer until thickened.
Season with salt and pepper.
Fold in noodles and shredded chicken.
Transfer to baking dish and top with cheese.
Combine breadcrumbs with olive oil and scatter over cheese.
Bake uncovered 20-25 minutes until golden and bubbling.
Rest 5-10 minutes before serving.