Heat olive oil in a large pot.
Add onion and cook until translucent.
Stir in garlic and tomato paste.
Add carrots, celery, and potatoes.
Sauté for five minutes, stirring often.
Add chopped prime rib and mix.
Pour in the beef broth slowly.
Add thyme, salt, pepper, and bay leaf.
Bring soup to a gentle boil.
Reduce heat and simmer 45 minutes.
Remove bay leaf before serving.
Garnish with chopped parsley.