Season the beef tenderloin tips with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Add the beef tips and sear until browned on all sides, about 5 minutes. Remove from skillet and set aside.
In the same skillet, add the sliced onions and mushrooms. Cook until the onions are translucent and the mushrooms are browned, about 5 minutes.
Stir in butter and flour through the onions and mushrooms, cooking for 1 minute until the flour is no longer raw.
Gradually add beef broth and Worcestershire sauce, stirring continuously. Bring to a simmer and allow the sauce to thicken slightly, about 3 minutes.
Return the beef tips to the skillet. Reduce heat to low and simmer for 10 minutes, or until the beef is tender and the sauce has thickened to your liking.
Adjust seasoning with salt and pepper, and serve hot.