Pat the beef stew meat dry with paper towels and season with salt and black pepper.
Heat olive oil in a large pot or Dutch oven over medium-high heat.
Add the beef stew meat in batches, browning all sides for about 5 minutes per batch. Remove browned beef and set aside.
In the same pot, add diced onion and cook for 4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the onions and garlic, stirring constantly for 2 minutes to cook the flour.
Gradually stir in the beef broth and water, scraping the bottom of the pot to release browned bits.
Return the browned beef to the pot.
Stir in tomato paste, dried thyme, dried rosemary, and bay leaves.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 1 hour 45 minutes.
Add the carrots, celery, and potatoes to the pot. Continue to simmer covered for an additional 45 minutes, or until vegetables and beef are tender.
Stir in frozen green peas and cook uncovered for 5 more minutes.
Remove bay leaves and adjust seasoning with salt and black pepper as needed.
Serve hot.