Prepare the Hamburger Steaks : In a large bowl, combine ground beef, egg, breadcrumbs, diced onion, salt, and black pepper. Mix until just combined; do not overmix. Form the mixture into 4–6 evenly-sized patties.Heat olive oil in a large skillet over medium-high heat. Remove from the skillet and set aside.

Prepare the Creamy Dill Sauce: In the same pan, melt butter over medium heat. Add the sliced onion and sauté for about 3-4 minutes until it softens. Stir in the minced garlic and cook for another minute. Sprinkle in the flour, stirring continuously for 1-2 minutes to form a paste. Slowly pour in the chicken broth and cream, whisking until the sauce is silky smooth. Add the fresh dill, and season with salt and pepper to taste. Let the sauce simmer for 5 minutes, allowing it to thicken to your desired consistency.

Combine and Serve : Return the cooked hamburger steaks to the skillet, spooning the sauce over the top. Simmer for 3–5 minutes, allowing the flavors to meld. Serve hot, garnished with additional fresh dill, alongside mashed potatoes, rice, or vegetables.