In a large sauce pan or stock pot, heat olive oil. Add onion, carrots and garlic. Season with salt and pepper to taste. Cook for 3-5 minutes, until onions are translucent. Stir in barley and potatoes.
Pour in the beef stock and canned tomatoes. Bring to a boil. Cover, reduce heat and simmer until potatoes and barley are tender, about 30 minutes.
Add the peas and cooked ground beef to the pot. Season with Italian seasoning and additional salt and pepper, if desired. Simmer an additional 5-10 minutes and serve.