Season the beef chunks with salt and pepper and dust them lightly with flour. Heat the olive oil in a large pan over medium-high heat. Sear the beef in batches, without crowding the pan, for 3 to 4 minutes per side, until deeply browned all over. Do not skip the searing — the browned crust is where most of the stew's flavour comes from. Move the seared beef into the slow cooker.
Turn the heat down to medium. Add the onion to the same pan and cook for 4 minutes, until soft. Stir in the garlic and tomato paste and cook for 1 minute, until the paste darkens slightly.
Pour in the red wine and scrape up the browned bits from the bottom of the pan with a wooden spoon. Simmer for 2 minutes, then pour the whole pan into the slow cooker.
Add the beef stock, carrots, mushrooms, bay leaves, and thyme to the slow cooker. Stir once, then put the lid on. Cook on low for 7 to 8 hours, or on high for 4 to 5 hours, until the beef is tender enough to fall apart with a fork. Keep the lid on and do not open the slow cooker to check it — every time you lift the lid, heat escapes and the cooking time stretches out.
One hour before serving, stir in the pearl barley. Put the lid back on and cook for 60 to 90 minutes more, until the barley is plump and chewy. Check the barley before serving — it should be tender but still have a bite.
Take out the bay leaves. Taste the stew and add salt and pepper if needed. If the broth is thinner than you like, take the lid off for the last 20 minutes so it reduces a little. Serve in deep bowls with chopped parsley on top and crusty bread on the side.