In a mixing bowl, combine grated onion, ground beef, breadcrumbs, salt, pepper, heavy cream, and egg. Mix gently until just combined. Divide into four portions and shape into patties.

Heat a skillet over medium heat; add olive oil and butter. Sear patties for 4-5 minutes on each side until golden brown. Remove from skillet.

In the same skillet, add minced garlic and diced onion, sauté for 2 minutes. Add salt, pepper, and flour to form a roux. Pour in chicken broth, simmer for 2 minutes.

Stir in heavy cream and dill, let it boil until thickened, about 2 minutes. Return hamburger steaks to the skillet, simmer for 5-6 minutes.