Crumble ground beef into a large bowl and mix in breadcrumbs, egg, Worcestershire sauce, garlic, sage, black pepper, and salt.
Once well combined, form the hamburger mixture into four equal oval patties.
Set a 12" skillet over medium heat and add the hamburger patties. Cook until a brown crust forms, then flip and repeat. Remove the patties from the skillet before they are completely cooked through.
Add onion slices to the drippings in the skillet and saute until tender and translucent. Then remove and set aside.
Turn the heat to low and prepare the gravy by melting butter into the skillet and sprinkling in flour. Continue to whisk this mixture for 5 minutes to prevent burning and allow the raw flour taste to cook out.
Slowly add dribbles of beef broth to the mixture while continuing to stir.
Once all beef broth has been added return the onion and hamburger steaks to the skillet. Let simmer until steaks are cooked though and gravy has thickened. Taste for salt and pepper and adjust as needed prior to serving.
Serve the cooked patties topped with sauted onions and a generous helping of gravy.