Heat the olive oil in a large pot over medium-high heat. Add the beef and cook until browned on all sides, about 6 minutes. Remove the beef and set it aside.
Add the onion, carrots, potatoes, and celery to the same pot. Cook for 5 minutes, stirring often, until the vegetables start to soften.
Stir in the garlic and cook for 1 minute. Add the tomato paste and stir to coat the vegetables.
Return the beef to the pot. Pour in the beef broth and add the thyme, bay leaves, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 1 hour and 30 minutes until the beef is tender and the broth has thickened.
While the stew simmers, cut a circle from the top of each sourdough bread bowl and hollow out the center, leaving a 1-inch wall.
Ladle the hot stew into the prepared bread bowls just before serving. Discard the bay leaves.