In a nonstick skillet, heat oil over medium high heat. Pat roast dry with paper towel and brown in skillet on all sides. Transfer to slow cooker.
Reduce heat to medium. Add onions and celery and cook, stirring until softened. Add garlic, thyme, salt and pepper and cook, stirring for one minute. Add flour and cook, stirring for 1 more minute. Add beef broth and bay leaf and cook, stirring until thickened.
Pour mixture over roast. Cover and cook on low for 10-12 hours or on high for 5-6 hours, until meat is tender. Stir green peppers and steak sauce into gravy. Cover and cook on high for 30 minutes until peppers are soft. To serve, discard bay leaf, place roast on platter and spoon sauce over.