In a non-stick skillet, brown meat for about 10 minutes, stirring frequently. Drain any excess fat. Place meat in a bowl & set aside.
Using the same skillet, saute the onions in olive oil until soft and slightly brown.
Return the meat to the skillet with the onions. Add salt, pepper, allspice, basil, oregano, and garlic. Cover & cook 10 more minutes.
In a large pot, add the green beans. Pour the canned tomatoes, and the diluted tomato paste over the green beans; stir.
Add the meat mixture to the green beans. Mix together.
Bring to a gentle boil, then cover and simmer for 1 hour, or until beans are tender. Add a little more water or stock, as needed.
Serve with rice or bulgur pilaf.