In a spacious bowl, combine the grated onion, ground beef, breadcrumbs, salt, pepper, heavy cream, and egg. Gently mix until just combined. Divide the mixture into four equal portions, rolling them into balls and then flattening each to about ¾ inch thick.

Heat a large skillet over medium heat and add olive oil and unsalted butter. Once hot, sear the hamburger steaks for 4-5 minutes on each side until golden-brown. Transfer to a plate and keep warm.

In the same skillet, add minced garlic and diced onion. Sauté for about 2 minutes until the onion becomes translucent. Sprinkle in salt, pepper, and flour, stirring to create a roux.

Pour in chicken broth while scraping the browned bits from the skillet. Allow to simmer for about 2 minutes until thickened.

Stir in heavy cream and fresh dill, raising the heat to bring to a delicate boil. Simmer for 1-2 minutes until thickened to desired consistency.

Return the seared hamburger steaks to the skillet, allowing them to reheat in the creamy dill sauce for 5-6 minutes. Serve warm.