In a large bowl, combine grated onion, ground beef, breadcrumbs, salt, black pepper, heavy cream, and egg. Gently mix until just combined to avoid tough patties. Shape into 4 balls and flatten into ¾-inch thick patties.

Heat 1 tablespoon of olive oil and 1 tablespoon of unsalted butter in a skillet over medium heat. Once melted, add the hamburger patties. Sear for 4-5 minutes on each side until golden brown. Remove and keep warm.

In the same skillet, add minced garlic and diced onion to the remaining drippings. Sauté for about 2 minutes until fragrant.

Stir in salt, black pepper, and flour. Cook for 1 minute while stirring. Gradually pour in chicken broth, scraping the bottom to deglaze. Let it simmer for 2 minutes to thicken.

Add heavy cream and fresh dill, stirring continuously. Cook for an additional 3-4 minutes until sauce thickens.

Return the seared patties to the skillet, nestling them in the sauce. Simmer on low for 5-6 minutes, flipping halfway through.