Divide the meat into 4 1/2"-thick patties. Season both sides with salt and pepper. Set aside.

Swirl 2 teaspoons in olive oil in a large non-stick skillet over medium heat. When the oil is hot, add the patties and cook for 4-5 minutes and then flip and cook for another 4-5 minutes or until cooked through. Remove the patties from the pan and set aside.

Heat the teaspoon of butter in the skillet. When melted, add the onions and sprinkle lightly with salt and freshly ground pepper. Cook, stirring frequently, until they become tender and start to caramelize, about 5-7 minutes (you may need to add an additional teaspoon of oil if the onions are burning or sticking). Add the mushrooms and garlic and cook until the mushrooms are tender, being careful not to let the garlic scorch.

When the onions and mushrooms are cooked, sprinkle them with 1 tablespoon of flour and stir quickly to combine. Add the broth and vinegar and cook until thickened. Add the beef patties and heat through. Serve each patty over mashed potatoes and top with mushrooms, onions, and gravy.