Pat the beef stew meat dry with paper towels to ensure proper browning.
Heat olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the beef stew meat in batches, avoiding overcrowding, and brown on all sides, about 4-5 minutes per batch. Remove browned beef and set aside.
In the same pot, add the diced onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Return the browned beef to the pot and stir in the tomato paste, coating the meat evenly.
Pour in the beef broth and water, scraping the bottom of the pot to release any browned bits.
Add the dried thyme, dried rosemary, bay leaves, salt, and black pepper. Stir to combine.
Bring the stew to a boil, then reduce heat to low and cover. Simmer gently for 1 hour and 45 minutes, stirring occasionally.
Add the sliced carrots, celery, and potatoes to the pot. Cover and continue to simmer for an additional 45 minutes, or until vegetables and beef are tender.
In a small bowl, whisk together the all-purpose flour and cold water until smooth to create a slurry.
Stir the slurry into the stew and cook uncovered for 5-10 minutes until the stew thickens.
Remove bay leaves and adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with chopped fresh parsley.