Dice the yellow onion and mince the garlic cloves, setting them aside for later.

In a large mixing bowl, combine ground beef, egg, salt, black pepper, dried onion, breadcrumbs, and Dijon mustard. Mix gently until just combined, then shape into four patties.

Heat a large skillet over medium-high heat and add olive oil and unsalted butter. Once hot, sear the patties for about 5 minutes on each side until golden-brown.

Reduce heat to medium. Add diced onion and minced garlic, seasoning with salt and pepper. Sauté for about 3 minutes until soft, then pour in dry white wine and let simmer for 2 minutes.

Stir in heavy cream and bring to a gentle boil. Add grated Parmesan and horseradish, mixing until melted. Adjust seasoning.

Return cooked patties to the skillet, coating with sauce. Simmer for an additional 5 minutes and garnish with chopped chives.