Heat oil in a large skillet over medium-high heat. Add onions and cook for 5 minutes or until golden. Add mushrooms and salt, cook 5 minutes more, stirring constantly. Add vinegar, remove mixture from pan and set aside.
Combine paprika through ground round and mix well. Shape ground round into 4 equal patties.
Grill 4 minutes on each side, or until done.
Place burgers on plates and top with onion/mushroom mixture, serve.