Brown the Beef and Onion: In a large skillet, heat a drizzle of oil over medium heat. Add the lean ground beef along with the diced medium onion, salt, and ground black pepper. Cook for about 5 to 7 minutes, stirring frequently, until the beef is browned and crumbled while the onion becomes translucent.

Add the Creamy Sauce: Reduce heat to medium-low and pour in the cream of mushroom soup, stirring to combine. Add cubed Velveeta cheese and let it melt into the mixture. Stir for approximately 3 to 5 minutes until the cheese is fully melted and creamy.

Assemble the Sandwiches: Pile a generous spoonful of the filling onto each hamburger bun. Customize with your favorite toppings like pickles or sliced tomatoes. Serve immediately.