Grate the onion into a large bowl. Add ground beef, breadcrumbs, salt, pepper, heavy cream, and egg. Mix until just combined.
Divide the beef mixture into 4 portions. Shape each into a ball, then flatten to about ¾ inch thick. Set aside.
Chop the onion, mince the garlic, and chop the dill finely.
Heat olive oil and butter in a large nonstick skillet over medium heat. Cook hamburger steaks 4-5 minutes per side until golden brown, then transfer to a plate.
Add garlic and diced onion to the skillet, reduce heat to low, and cook until fragrant, about 2 minutes.
Stir in salt, pepper, and flour until combined. Pour in chicken broth and simmer for 2 minutes, scraping browned bits from the skillet.
Add heavy cream and chopped dill. Bring to a boil, then simmer for 1-2 minutes until the sauce thickens.
Return hamburger steaks to the skillet and simmer for 5-6 minutes until heated through and cooked in the center.
Finish with additional dill and freshly ground black pepper. Serve warm.