In a large bowl, combine the ground beef, breadcrumbs, milk, egg, garlic powder, onion powder, salt, and black pepper. Mix until just combined.
Shape the mixture into 4 equal patties.
Heat the olive oil in a large skillet over medium heat. Add the hamburger patties and cook for about 5-6 minutes on each side, or until browned and cooked through. Remove the patties from the skillet and set aside.
In the same skillet, melt the butter over medium heat. Add the beef broth and bring to a simmer.
Stir in the heavy cream, dill, Worcestershire sauce, and season with salt and pepper. Let the sauce simmer for about 3-4 minutes until it thickens slightly.
Return the hamburger patties to the skillet, spoon the sauce over them, and cook for an additional 2 minutes to heat through.
Serve the hamburger steaks hot, drizzled with the creamy dill sauce.