Place the beef cubes in the slow cooker. Add the carrots, celery, onion, and garlic on top.
In a small bowl, whisk the beef broth with the tomato paste, Worcestershire sauce, thyme, salt, pepper, and flour until smooth. Pour this mixture over the beef and vegetables. Add the bay leaves.
Cover and cook on low for 8 hours until the beef is very tender.
About 30 minutes before the stew is done, place the potatoes in a large pot and cover with water. Bring to a boil and cook until the potatoes are fork-tender, about 15 minutes.
Drain the potatoes and return them to the pot. Add the butter and milk, then mash until smooth and creamy. Season with a pinch of salt if needed.
Remove the bay leaves from the stew. Serve the stew in bowls with a scoop of mashed potatoes on the side or on top.