Heat 2 tbs oil in a large Dutch oven over medium high heat until just smoking.
Season the beef liberally with salt and pepper and toss into the pot. Cook until just browned on all sides, about 5 minutes. Remove from the pot and set aside.
Reduce the heat to medium, add the remaining 1 tbs oil, and cook the onions, carrots, and celery. Cook for 5 minutes, until starting to brown. Add the mushrooms and cook 5 to 7 minutes longer until water has evaporated from the mushrooms.
Stir in the tomato paste and cook for 1 minute until toasted. Deglaze the pan with the wine and add the bay leaves, thyme, and beef stock. Bring to a boil and add the barley. Keep the temperature at a simmer and cook 45 minutes longer. Return the beef, and any accumulated juices, to the pot. Cook 10 minutes longer to heat through.
Sprinkle with parsley and ladle into bowls.