Combine ground beef, bread crumbs, French onion soup mix, ground mustard, egg, and Worcestershire sauce in a mixing bowl.

Mix ingredients with a spatula, fork, or spoon until just combined. Do not use hands.

Form the mixture into four large patties (about 125g each). If the mixture is sticky, wet your hands slightly.

Heat olive oil in a saute pan over medium to medium-high heat.

Sear the hamburger steaks for 1-2 minutes on each side until lightly browned. Remove from pan and set aside.

Add butter to the same saute pan and melt over medium heat, scraping up any fond from the bottom.

Add chopped onion and sliced mushrooms to the pan. Saute for 10 minutes, scraping the bottom of the pan occasionally.

Add minced garlic and saute for about 2 minutes until fragrant, being careful not to burn it.

Add red wine and reduce over medium to medium-high heat for approximately 10 minutes until mostly reduced.

Clear a well in the center of the pan, add butter, and melt over medium heat.

Add flour to the melted butter and whisk to form a roux. Cook for 2-3 minutes, stirring occasionally.

Slowly mix in the onion, mushroom, and garlic mixture into the roux.

Gradually whisk in the beef broth.

Add Worcestershire sauce, soy sauce, and ketchup. Stir to combine.

Bring the gravy to a simmer over medium to medium-high heat, scraping the bottom of the pan.

Return the seared hamburger steaks to the gravy.

Simmer uncovered for 10-15 minutes, flipping the steaks occasionally, until the steaks are cooked through and the gravy is thick.

Taste and adjust seasoning with salt and pepper if necessary.