Cook the Onion and Garlic Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the minced onion and garlic and sauté for about 5 minutes until softened. Remove from the pan and set aside to cool completely. This step is optional but gives the patties a more subtle, integrated flavor.
Make the Panade In a large bowl, whisk together the egg, milk, mustard, ketchup, Worcestershire sauce, oregano, salt, and pepper. Stir in the breadcrumbs and continue stirring until the mixture forms a paste. Add the cooled onion and garlic and stir to combine.
Mix the Beef Add the ground beef to the bowl with the panade. Use your hands to mix until just combined, stopping as soon as the mixture is uniform. Do not overmix or the patties will be tough.
Shape and Chill Divide the mixture into 4 equal portions and form each into an oval patty about 3/4 inch thick. Place them on a plate, cover, and refrigerate for 15 minutes to help them hold their shape during cooking.
Sear the Patties Heat the remaining 2 tablespoons of olive oil in the same skillet over medium-high heat. Sear the patties two at a time for 1 minute per side until browned on the outside. Remove and set aside. The centers will still be raw at this point.
Build the Gravy Add 1 tablespoon of olive oil to the same skillet over medium heat. Sauté the diced onion for 5 minutes. Add the butter and sliced mushrooms and cook for another 5 minutes until the mushrooms are golden.
Add the Liquid Pour in the beef broth and add the bouillon cube, onion powder, garlic powder, and Worcestershire sauce. Stir to combine and bring the gravy to a boil.
Thicken the Gravy Whisk the cornstarch into the cold water until smooth. Slowly pour the slurry into the boiling gravy while whisking continuously, adding only as much as needed to reach your desired consistency. Reduce the heat to medium.
Finish Cooking the Steaks Return the seared patties to the skillet and spoon the gravy over the top. Cover and cook over medium heat for 10 to 15 minutes, until the internal temperature of the patties reaches 160 degrees Fahrenheit.
Serve Spoon generously with mushroom gravy and serve over mashed potatoes or alongside buttered egg noodles.