Brown the ground beef in a large pot over medium heat, breaking it up with a spoon until no pink remains. Drain excess fat if needed and set the beef 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 tomato paste. Cook for 1 minute until the paste darkens slightly.
Return the ground beef to the pot. Add the barley, diced tomatoes with their juice, beef broth, thyme, and bay leaves.
Bring the mixture to a boil, then reduce to a simmer. Cover and cook for 45 minutes, stirring occasionally, until the barley is tender.
Remove the bay leaves. Taste and adjust salt and pepper as needed before serving.