Place all hamburger steak ingredients, except oil, in a bowl and gently mix to combine. Form meat mixture into 4, 3/4 inch thick, oval patties. Heat oil in a non-stock skillet set over medium-high heat. Cook burgers 4-5 minutes per side, or until entirely cooked through.
To make the gravy, heat oil in a pot set over medium-high heat. Add onions and mushrooms and cook until tender. Mix in flour. Slowly mix in the stock. Bring to a simmer and cook until gravy thickens. Season with salt and pepper.
Serve gravy on or alongside the hamburger steaks.