[I think this is too much beef, and in too large pieces. I would settle for half the quantity, cut or chopped into much smaller morsels. And I have decided that a twig of fresh or dried rosemary is a happy herb to add and then fish out at the last. And I like green pepper, in slivers or squares.]
Sauté the onion, garlic, carrot, and celery in the oil until they are relaxed and beginning to be brown. Add the tomatoes, spices, and herbs (thyme, marjoram, basil).
Soak the mushrooms in hot water until tender. Cut into small pieces, strain the water, and add it all to the sauce. Cover, and let simmer for 3 to 4 hours.
Brown the beef in a little fat or oil. Add a little boiling water or stock and let simmer until tender. Add to the sauce about 1 hour before serving, so that the two may marry their flavors.
Serve in a large bowl, to be poured [ladled is a better word here] over the sliced polenta on each plate.