In large bowl, whisk together flour, salt and pepper. Add beef; toss to coat.
In large Dutch oven, heat 1 tbsp of the butter and half of the oil over medium heat until melted; cook half of the beef mixture, stirring occasionally, until browned, about 10 minutes. Using slotted spoon, transfer to bowl. Repeat with 1 tbsp of the remaining butter and the remaining oil and beef mixture.
In same pan, melt remaining butter over medium heat; cook mushrooms, celery and onion, stirring occasionally, until softened, about 5 minutes. Add tomato paste; cook, stirring, for 2 minutes. Pour in wine; cook, stirring and scraping up browned bits, for 2 minutes.
Return beef mixture and any accumulated juices to pan. Add potatoes, carrots, thyme, parsley, bay leaves, broth and Worcestershire sauce; bring to boil, stirring occasionally and scraping to loosen any remaining browned bits.
Cover and braise in 350°F oven for 45 minutes. Uncover and cook until vegetables are tender and beef offers no resistance when pierced with tip of knife, 30 to 40 minutes. Stir in peas; cook for 5 minutes.
Skim any fat from surface of stew; discard thyme, parsley and bay leaves. Let stand for 10 minutes before serving.