Whisk together 3/4 cup flour, salt and pepper in a shallow pie plate. While oil is heating in Dutch oven, dredge stew meat in flour mixture. Cook beef in hot oil for about 6 minutes per batch to brown.
With the beef reserved on a plate, cook the onion in the same oil in the Dutch oven for about 6 minutes, stirring. Add beef broth, bay leaf, and the browned beef.
Bring stew to a boil, then simmer covered on low for 1 hour. Add vegetables and simmer for 2 more hours.
Chop the celery and carrots after you've set the stew to simmer the first time.