In a large mixing bowl, combine the ground beef, breadcrumbs, beaten egg, diced onion, salt, and black pepper. Use your hands to gently mix until everything is incorporated, being careful not to overwork the meat. Form mixture into 6-8 oval patties about ¾ inch thick and let rest while heating the skillet.

Heat an oven-safe skillet over medium-high heat until hot, then add a small amount of oil to lightly coat the pan. Place patties in the skillet and cook for 3-4 minutes on each side until golden brown and cooked through. Remove patties from skillet and set aside.

In the same skillet, reduce heat to medium and add butter. Once melted, add sliced onions and sauté for 5-7 minutes until softened and translucent. Sprinkle flour over onions, stirring constantly for about 2 minutes to cook without browning.

Gradually whisk in beef broth and heavy cream, ensuring no lumps remain. Stir for 3-4 minutes as mixture comes to a gentle boil and thickens into a rich gravy.

Nestle the browned hamburger patties back into the skillet, ensuring they are submerged in gravy. Cover tightly with aluminum foil and transfer to a preheated oven at 350°F. Bake for 45 minutes, then remove foil and bake an additional 15 minutes.

After baking, remove from oven and let rest for 10 minutes before serving to allow gravy to thicken.