Prepare the Patties: In a large bowl, combine the ground beef, breadcrumbs, egg, ketchup, Worcestershire sauce, Dijon mustard, garlic powder, onion powder, salt, and pepper. Mix until just combined; avoid overmixing to prevent tough patties. Divide the mixture into 4 equal portions and shape each into an oval patty, approximately ¾-inch thick.

Sear the Patties: Heat the olive oil in a large skillet over medium-high heat. Add the patties and cook for about 3 minutes on each side, or until browned. Transfer the patties to a plate and set aside.

Sauté the Vegetables: In the same skillet, reduce the heat to medium and add the butter. Once melted, add the chopped onion and cook until translucent, about 2 minutes. Add the minced garlic and sliced mushrooms; cook until the mushrooms are browned and have released their moisture, approximately 5 minutes.

Make the Gravy: Sprinkle the flour over the sautéed vegetables, stirring constantly for about 1 minute to cook out the raw flour taste. Gradually whisk in the beef broth, ensuring a smooth consistency. Stir in the ketchup and Worcestershire sauce. Bring the mixture to a simmer, allowing it to thicken slightly. Season with salt and freshly ground black pepper to taste.

Combine Patties and Gravy: Return the seared patties to the skillet, nestling them into the gravy. Reduce the heat to low, cover, and simmer for about 10 minutes, or until the patties are cooked through and the gravy has thickened to your liking.

Serve: Plate the Salisbury Steaks and generously spoon the mushroom gravy over each patty. Serve hot alongside mashed potatoes, buttered noodles, or your preferred side dish.