Sauté onions in oil over medium heat until golden brown, about 5 minutes.

In a large bowl, combine half of the sautéed onions, ground beef, ground turkey, bread crumbs, egg, egg white, 0.25 cup beef broth, salt, and black pepper. Shape into 8 oval patties.

In a large deep skillet over medium-high heat, brown both sides of patties, about 4 to 5 minutes on each side. Set aside on a dish.

Add mushrooms to the skillet, season with salt and pepper, and sauté 2-3 minutes.

Return patties to the skillet with the mushrooms.

In a small bowl, blend flour and remaining broth until smooth. Mix in remaining onions, tomato paste, vinegar, water, Worcestershire sauce, and mustard powder. Pour over meat and mushrooms.

Cover and cook on low heat for 20 minutes, stirring occasionally.