Heat olive oil in a skillet over medium-high heat. Sear beef tips until browned on all sides; season with salt and pepper.
Remove beef and sauté onions and garlic in the same skillet until soft.
Sprinkle flour over onions and garlic; stir for two minutes before gradually whisking in broth.
Return beef to the skillet, add Worcestershire sauce, bring to a simmer, cover, and cook for 20 minutes.
For thicker gravy, remove the lid during the last 5 minutes of cooking.
Serve over mashed potatoes or rice, drizzling extra sauce on top.