In a large bowl, combine the grated onion, ground beef, breadcrumbs, salt, pepper, heavy cream, and the egg. Mix gently until just combined.

Divide the beef mixture into four equal portions and shape into patties about ¾ inch thick, making a slight indentation in the center.

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

In the same skillet, add diced yellow onion and minced garlic, sautéing for about 2 minutes until fragrant.

Sprinkle salt, pepper, and flour, stir to combine, and gradually pour in chicken broth, letting it simmer until slightly thickened.

Slowly pour in the heavy cream and add chopped dill, bringing the sauce to a gentle boil before lowering it to simmer.

Return the hamburger steaks to the skillet, allowing them to simmer gently in the sauce for 5-6 minutes.

Remove from heat and serve immediately, ladling sauce over each patty.