In a large bowl, combine the ground beef, breadcrumbs, milk, finely chopped onion, beaten egg, garlic powder, Worcestershire sauce, salt, and pepper. Mix gently until just combined. Form into 4 oval-shaped patties about 1 inch thick. Set aside.

Heat butter and olive oil in a large skillet over medium-low heat. Add the sliced onions and a pinch of salt. Stir frequently and cook slowly for 20-25 minutes until onions are deep amber and caramelized. Add minced garlic and cook for another 1-2 minutes.

Push the onions to one side of the pan. Increase heat to medium-high and add the patties. Cook 3-4 minutes per side until browned but not fully cooked. Remove patties and set aside.

Lower heat to medium. Sprinkle flour over onions and stir well. Cook 1-2 minutes to remove raw flour taste. Gradually whisk in beef broth, scraping the bottom of the pan. Add Worcestershire sauce and bring to a gentle simmer. Season with salt and pepper. Cook 5-7 minutes until gravy thickens.

Return patties to the pan and nestle into the gravy. Reduce heat to low, cover, and simmer for 10-12 minutes until patties reach an internal temperature of 160°F (71°C).

Garnish with chopped parsley if desired. Serve hot over mashed potatoes or buttered egg noodles.