In a large bowl, toss the beef cubes with flour, salt, and pepper until each piece is lightly coated. This helps thicken the stew naturally as it cooks and creates a nice crust on the meat.
Heat olive oil in a large pot or Dutch oven over medium-high heat. Add the beef in batches, making sure not to crowd the pan. Brown the meat on all sides, then remove it from the pot and set it aside on a plate.
In the same pot, add the chopped onion and celery. Cook for about 5 minutes until the onions are translucent. Add the garlic and cook for an additional minute until fragrant, being careful not to burn it.
Stir in the tomato paste and then pour in the beef broth. Use a wooden spoon to scrape up any browned bits from the bottom of the pot. Return the beef to the pot and add the thyme and rosemary. Bring to a boil, then reduce heat to low, cover, and simmer for 1 hour.
After the initial hour, add the carrots and potatoes to the pot. Cover and continue to simmer for another 45 to 60 minutes, or until the beef and vegetables are completely tender.
Stir in the frozen peas and cook for 5 more minutes until heated through. Taste the stew and adjust the salt and pepper if necessary. Garnish with fresh parsley before serving.