Pat the beef dry with paper towels and season generously with salt and pepper. Drying the beef helps it brown better.
In a large Dutch oven or heavy pot, heat the olive oil over medium-high heat. Add the beef in batches, searing on all sides until browned. Remove and set aside.
Add the onion and celery to the pot, cooking until softened, about 5 minutes. Stir in garlic and cook for 1 more minute until fragrant.
Sprinkle in the flour and stir to coat the vegetables. This helps thicken the stew later.
Add the tomato paste and stir until well blended. Pour in the red wine, scraping up the browned bits from the bottom of the pot for extra flavor.
Return the beef to the pot. Add the broth, Worcestershire sauce, thyme, and bay leaves. Bring to a simmer.
Reduce heat to low, cover, and let cook gently for 1 ½ to 2 hours, stirring occasionally, until the beef is tender.
Add the carrots and potatoes. Continue simmering for 30 minutes, or until vegetables are fork-tender.
Taste and adjust seasoning with more salt and pepper if needed. Stir in peas at the very end if using.
Remove bay leaves, garnish with parsley, and serve hot.