Heat the olive oil in a large Dutch oven over medium-high heat. Add the lamb chunks and brown them on all sides for about 6 minutes. Remove the lamb and set it aside.
Add the onion, carrots, and garlic to the pot. Cook for 4 minutes until the onion softens.
Stir in the tomato paste and cook for 1 minute. Pour in the red wine and scrape the bottom of the pot to release any browned bits.
Return the lamb to the pot. Add the beef broth, thyme, bay leaves, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover, and simmer for 45 minutes.
Stir in the pearl barley and sliced mushrooms. Cover again and simmer for 40 more minutes until the barley is tender and the lamb is soft.
Remove the bay leaves. Taste and adjust seasoning if needed. Sprinkle with fresh parsley before serving.