Prepare the hamburger steaks:
In a large bowl, grate the onion. Add ground beef, breadcrumbs, salt, pepper, heavy cream, and egg. Mix with your hands until just combined.
Divide the mixture into 4 portions and shape each into a ball. Flatten the balls with the palm of your hand or a spatula until about 3/4 inch (2 cm) thick. Set aside.
Prepare the sauce ingredients:
Finely chop the remaining onion, mince the garlic, and chop the dill.
Cook the hamburger steaks:
Heat olive oil and butter over medium heat in a large nonstick skillet. Add the hamburger steaks and cook for 4-5 minutes per side until browned. Transfer the steaks to a clean plate and set aside.
Make the creamy dill sauce:
In the same skillet, reduce the heat to low and add the chopped onion and minced garlic. Cook for about 2 minutes until fragrant. Stir in the salt, pepper, and flour. Cook for 1 minute, stirring constantly.
Pour in the chicken broth, scraping up any browned bits from the skillet with a wooden spoon. Simmer for 2 minutes.
Finish the sauce and cook the steaks:
Add the heavy cream and chopped dill to the skillet, bringing the sauce to a boil. Simmer for 1-2 minutes until the sauce begins to thicken. Return the hamburger steaks to the skillet and simmer for 5-6 minutes, or until the steaks are heated through and no longer raw in the center.
Serve:
Garnish with extra dill and freshly grated black pepper. Serve the hamburger steaks with the creamy dill sauce over mashed potatoes, rice, or vegetables. Enjoy!