Preheat the oven to 325°F.
Cut the round steak into six approximately equal portions, about ¾ to 1 inch thick.
Arrange the steak pieces in a single layer in a deep 9×13-inch baking dish.
In a medium bowl, mix the condensed cream of mushroom soup and dry onion soup mix until combined.
Spoon the mushroom gravy mixture over the steak, covering each piece evenly.
Cover the baking dish tightly with aluminum foil or an oven-safe lid.
Bake for 2½ hours, checking for tenderness after two hours. Continue cooking for up to three hours if necessary, until the beef is fork-tender.
Remove the dish from the oven and allow it to stand for five minutes.
Place the sour cream in a small bowl. Gradually stir in several spoonfuls of warm gravy to temper it.
Gently stir the sour cream mixture into the baking dish until the sauce is smooth.
Spoon the creamy mushroom gravy over the beef and serve warm.