Step 1: In a large bowl, combine the ground beef, breadcrumbs, egg, 1/4 cup finely chopped onion, 1 tablespoon Worcestershire sauce, garlic powder, 1/2 teaspoon black pepper, and 1/2 teaspoon salt. Mix gently with your hands until just combined, being careful not to overmix.
Step 2: Divide the mixture into 4 equal portions and form each into an oval-shaped patty, about 1/2-inch thick.
Step 3: Heat olive oil in a large, oven-safe skillet (preferably cast iron) over medium-high heat. Once hot, carefully add the patties and sear for 3-4 minutes per side, until deeply browned. Remove the patties from the skillet and set aside.
Step 4: Reduce heat to medium. Add butter to the skillet. Add the sliced large onion and mushrooms, cooking for 5-7 minutes, stirring occasionally, until softened and lightly browned. Add minced garlic and cook for another minute until fragrant.
Step 5: Sprinkle flour over the onions and mushrooms. Cook, stirring constantly, for 1-2 minutes to create a roux, scraping up any browned bits from the bottom of the pan.
Step 6: Gradually whisk in the beef broth, ensuring no lumps form. Stir in 1 tablespoon Worcestershire sauce and Dijon mustard, and dried thyme. Bring the gravy to a simmer, stirring until it thickens.
Step 7: Return the seared patties to the skillet, nestling them into the gravy. Reduce heat to low, cover, and simmer for 15-20 minutes, or until the patties are cooked through and tender, and the gravy has thickened to your desired consistency.
Step 8: Taste the gravy and adjust salt and pepper as needed. Garnish with fresh chopped parsley, if desired, and serve hot with your favorite side dishes.