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

Divide the meat mixture into four equal portions and shape each into a ball, then flatten them gently into patties.

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

In the same skillet, add diced yellow onion and minced garlic. Sauté for about 2 minutes, then add flour and cook for 1 minute.

Gradually pour in the chicken broth while scraping the bottom of the skillet. Simmer until slightly thickened, then stir in cream and dill.

Return the patties to the skillet, spooning sauce over each patty. Simmer for 5-6 minutes, allowing flavors to meld.