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

Divide the mixture into four equal portions and shape into patties about ¾ inch thick. Set aside.

Heat a large skillet over medium heat with olive oil and unsalted butter. Sear the patties for 4-5 minutes on each side until golden brown. Remove from skillet.

In the same skillet, lower the heat and add diced yellow onion and minced garlic. Cook for about 2 minutes until fragrant.

Sprinkle salt and pepper over the onions, stir in all-purpose flour, and cook for 1 minute until roux forms.

Slowly add chicken broth while stirring to deglaze the pan. Simmer for about 2 minutes.

Add heavy cream and fresh dill, bring to a gentle boil, then reduce to a simmer for 3-4 minutes.

Return the patties to the skillet and let simmer for 5-6 minutes until heated through.