In a wide bowl, combine the ground beef, panko, egg, and spices. Work the mixture with your hands just until incorporated (don't over-mix or the meat will get tough). Form into 4 to 6 oval-shaped steaks, about ¾-inch thick.
Heat a cast-iron skillet over medium-high heat with a drizzle of oil. Brown the beef steaks for 3-4 minutes per side until a dark crust forms. They don’t need to be cooked through yet. Remove them from the pan and set aside on a plate.
In the same pan (keep those flavorful beef drippings!), melt the butter. Toss in the onion rings and sliced mushrooms. Cook them down for 8–10 minutes, stirring occasionally, until the onions are caramelized and the mushrooms are golden and tender.
Sprinkle the flour over the vegetables and stir constantly for one minute to toast the flour. Slowly pour in the beef bone broth and the balsamic vinegar, whisking or stirring to prevent any lumps from forming.
Once the gravy begins to thicken and bubble, nestle the beef steaks back into the pan, burying them under the onions and mushrooms.
Lower the heat to medium-low, cover the skillet, and let everything braise together for about 10 minutes. This allows the gravy to penetrate the meat, making it incredibly juicy. Serve hot, directly from the skillet.