Cook and drain your noodles, then set aside.
Melt butter and add celery, carrot, and onion. Cook 3 minutes and whisk in flour, salt, pepper, and thyme.
Add the chicken broth and milk, then bring to a boil and simmer until the sauce thickens.
Stir in cheese and ham, then remove from heat and stir in cooked noodles.
Transfer to a casserole dish and bake for 30 minutes, or until casserole is hot.