Preheat Oven: Preheat your oven to 350°F (175°C) and grease a 9×13-inch baking dish to prevent sticking. This ensures even cooking and easy cleanup when the dish is finished.
Make the Hamburger Steaks: In a large bowl, combine ground beef, breadcrumbs, egg, Worcestershire sauce, garlic powder, onion powder, salt, and pepper. Use your hands to gently mix the ingredients until well incorporated, being careful not to overmix which can make the patties tough. Shape the mixture into 4-6 evenly sized patties, pressing slightly in the center to prevent them from puffing up during cooking.
Brown the Steaks: Heat olive oil in a large skillet over medium heat until shimmering. Place the patties in the skillet without overcrowding and brown for 2-3 minutes per side until they develop a nice crust. You're not cooking them through at this point, just creating flavor through caramelization. Transfer the browned patties to the prepared baking dish.
Make the Sauce: Using the same skillet with the flavorful beef drippings, add the thinly sliced onion and minced garlic. Sauté for 3-4 minutes until softened and fragrant. Stir in the cream of mushroom soup, milk, sour cream, Worcestershire sauce, thyme (if using), salt, and pepper. Whisk together and simmer for 2-3 minutes until the sauce is smooth and slightly thickened.
Assemble & Bake: Pour the creamy sauce evenly over the hamburger steaks in the baking dish, making sure to coat all the patties. Cover the dish tightly with aluminum foil to trap moisture and heat. Bake for 30-35 minutes, or until the patties reach an internal temperature of 160°F (71°C) and the sauce is bubbling around the edges.
Serve: Remove from the oven and let the dish rest for 5-10 minutes before serving. This allows the juices to redistribute through the meat and the sauce to thicken slightly. Serve hot with mashed potatoes, rice, or egg noodles to soak up the delicious sauce.