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

Divide the mixture into four equal portions and roll each into a ball. Gently press down each ball to form patties about ¾ inch thick.

In a large skillet, heat olive oil and butter over medium heat until shimmering, about 2 minutes. Add the patties and cook for 4-5 minutes on each side until golden brown.

Using the same skillet, add minced garlic and diced onion; sauté for about 2 minutes until fragrant. Stir in salt, pepper, and flour, cooking for another minute.

Gradually whisk in the chicken broth, heating until the mixture simmers and slightly thickens, scraping up browned bits for flavor.

Lower the heat and stir in the heavy cream with freshly chopped dill until combined. Simmer for an additional 5-6 minutes, returning the patties to coat them.

Plate the Hamburger Steaks and spoon the creamy dill sauce over the top. Garnish with fresh dill and pepper.