Prepare the Beef: In a large bowl, toss the beef stew meat with flour, salt, and pepper until the meat is evenly coated.
Brown the Beef: Heat the vegetable oil in a large pot or Dutch oven over medium-high heat. Add the beef and brown on all sides, about 5-7 minutes. Remove the beef from the pot and set it aside.
Sauté the Vegetables: In the same pot, add the chopped onion and garlic. Sauté for 3-4 minutes until the onion is translucent and the garlic is fragrant.
Deglaze the Pot: Pour in the beef broth and water, scraping up any browned bits from the bottom of the pot. This will add extra flavor to the stew.
Add the Vegetables and Beef: Add the carrots, potatoes, celery, bay leaf, and thyme to the pot. Return the browned beef to the pot, and bring the mixture to a boil.
Simmer the Stew: Once boiling, reduce the heat to low, cover the pot, and let the stew simmer for 1.5 to 2 hours, or until the beef is tender and the vegetables are cooked through.
Add Peas and Finish: If using, add the peas to the stew in the last 10 minutes of cooking. Remove the bay leaf, and season the stew with additional salt and pepper to taste.
Serve: Ladle the stew into bowls, garnish with fresh parsley if desired, and serve hot with crusty bread.