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

Heat a large skillet over medium heat. Add olive oil and butter. Sear patties for 4-5 minutes on each side until golden-brown. Transfer to a plate and cover to keep warm.

In the same skillet, add minced garlic and additional diced onion, cooking for 2 minutes until fragrant. Stir in salt, black pepper, and all-purpose flour, mixing well.

Gradually pour in chicken broth while scraping the bottom of the skillet. Increase heat to medium, simmer for 2 minutes.

Add heavy cream and chopped dill, stirring well. Bring to a gentle boil, reduce heat to simmer for 1-2 minutes until thickened. Return patties to skillet and simmer for 5-6 minutes until heated through.