In a large mixing bowl, combine grated onion, ground beef, breadcrumbs, salt, black pepper, heavy cream, and egg. Gently mix until just combined, then shape into four patties.

Heat a large skillet over medium heat and add olive oil and butter. Once heated, sear the patties for 4-5 minutes per side until browned and cooked through. Remove and set aside.

In the same skillet, add diced onion and minced garlic. Cook over low heat until the onion is translucent and garlic is fragrant, about 2 minutes.

Sprinkle in flour, stirring quickly for about 30 seconds. Gradually pour in chicken broth, scraping the bottom of the skillet. Simmer for about 2 minutes until thickened.

Stir in heavy cream and fresh dill, bringing the sauce to a gentle boil and simmer for another 1-2 minutes until creamy.

Return patties to the skillet, simmer gently in the sauce for 5-6 minutes until heated through and coated.