Step 1: In a large bowl, combine the ground beef, breadcrumbs, egg, 1/4 cup finely minced yellow onion, 1 tablespoon Worcestershire sauce, 1 teaspoon garlic powder, 1 teaspoon salt, and 1/2 teaspoon black pepper. Gently mix with your hands until just combined; do not overmix.
Step 2: Divide the mixture into 6 equal portions and form each into an oval-shaped patty, about 3/4-inch thick. Create a slight indentation in the center of each patty with your thumb to prevent bulging during cooking.
Step 3: Heat 1 tablespoon of olive oil in a large skillet or cast-iron pan over medium-high heat. Once hot, carefully place the patties in the skillet (work in batches if necessary to avoid overcrowding). Sear for 3-4 minutes per side until deeply browned and a crust has formed. Remove the patties from the skillet and set aside.
Step 4: In the same skillet, reduce the heat to medium. Add 1 tablespoon of butter. Once melted, add the sliced mushrooms and 1/2 cup finely diced yellow onion. Sauté, stirring occasionally, for 5-7 minutes until the mushrooms are tender and browned, and the onions are softened.
Step 5: Sprinkle 2 tablespoons of all-purpose flour over the sautéed vegetables. Cook, stirring constantly, for 1-2 minutes to toast the flour and create a roux.
Step 6: Slowly whisk in 2 cups of beef broth, 1 tablespoon of Worcestershire sauce, 1 teaspoon of Dijon mustard, 1/2 teaspoon of garlic powder, and 1/4 teaspoon of black pepper. Continue whisking until the mixture is smooth and begins to thicken. Bring the gravy to a gentle simmer. Taste and adjust seasonings as needed.
Step 7: Return the seared Salisbury steak patties to the skillet, nestling them into the simmering gravy. Reduce the heat to low, cover the skillet, and let the patties simmer in the gravy for 10-15 minutes, or until they are cooked through to an internal temperature of 160°F (71°C). Spoon the rich mushroom gravy generously over each patty before serving.