01 -
Combine ground beef, eggs, breadcrumbs, and half of the onion soup mix in a large bowl. Mix until just combined, then shape into 4 to 6 patties depending on preferred size.
02 -
Heat olive oil in a large skillet over medium-high heat. Add patties and cook, flipping once, until internal temperature reaches 160°F (71°C), about 6 to 8 minutes per side depending on thickness. Cover skillet with a lid to speed cooking if desired.
03 -
Transfer cooked patties to a plate and set aside. Do not discard the drippings in the skillet.
04 -
Reduce heat to medium and add butter to the skillet. Once melted, whisk in the flour, remaining onion soup mix, and Worcestershire sauce. The mixture will be thick and lumpy—continue whisking to combine thoroughly.
05 -
Gradually whisk in water and milk to the flour mixture, ensuring all lumps dissolve. Cook until gravy thickens and reaches a smooth, velvety consistency.
06 -
Return the hamburger steaks to the skillet, coating them evenly with the gravy. Heat through briefly and serve immediately.