Toss the beef stew meat with the flour until lightly coated. Heat the vegetable oil in a large pot over medium-high heat and brown the beef in batches. Remove the beef and set it aside.
Add the onion, carrots, and celery to the same pot. Cook for 5 minutes until the vegetables begin to soften. Stir in the garlic and cook for 1 minute more.
Return the beef to the pot. Pour in the beef broth and add the potatoes, bay leaves, thyme, salt, and pepper. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 1 hour and 30 minutes until the beef is tender.
While the stew simmers, cook the egg noodles in a separate pot according to package directions. Drain the noodles and return them to the pot. Stir in the butter until it melts and coats the noodles evenly.
Remove the bay leaves from the stew. Serve the stew ladled over the buttered egg noodles.