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

Heat a large skillet over medium heat with olive oil and unsalted butter. Cook the hamburger patties for 4-5 minutes on each side until browned.

In the same skillet, add minced garlic and diced onions, sauté for 2 minutes. Sprinkle in flour and stir until absorbed.

Deglaze with low sodium chicken broth, scraping the skillet's bottom and simmer until thickened, about 2 minutes.

Reduce heat, add heavy cream and fresh dill, cooking for 1-2 minutes until the sauce thickens slightly.

Return seared hamburger steaks to the skillet and simmer for 5-6 minutes, ensuring they are cooked through.