Mix the patties. In a large bowl, combine the ground beef, onion, garlic, egg, breadcrumbs, Worcestershire, ketchup, and seasoning. Mix just until combined (don’t overwork it). Shape into 4–6 oval patties.
Sear. Heat a large skillet over high heat. Add a little oil if needed. Sear patties 1–2 minutes per side until browned. Transfer to a plate.
Cook onions and mushrooms. Reduce heat to medium-high. Add oil if the pan looks dry. Add onions, cook 2 minutes. Add mushrooms and Worcestershire, stir once, then cook 4–5 minutes mostly undisturbed to brown. Add garlic and cook 1 minute.
Make the roux. Add butter. Once melted, sprinkle flour over mushrooms/onions and stir. Cook 2–3 minutes.
Finish the gravy. Slowly stir in beef broth. Add Dijon and black pepper. Bring to a simmer.
Simmer patties. Add patties back to the skillet. Simmer 10 minutes, flipping halfway, until cooked through. Taste and adjust salt.
Toast the bread. Butter both sides of the Texas toast. Toast in a skillet over medium heat until golden. Add cheese during the last minute if using.
Assemble. Place toast on plates, top with a patty, spoon gravy over the top, garnish if you’d like, and serve hot.