In a large bowl, whisk together the milk, potato flakes, Worcestershire sauce, grill seasoning and salt.
Add the beef and mix until well combined. Divide the meat mixture into four patties. Refrigerate for 30 minutes (or up to four hours).
In a large, non-stick skillet, melt two tablespoons of the butter over medium heat. Add the salisbury steaks and cook about five minutes per side to brown the outside. Remove to a clean plate and tent with foil.
Add the remaining two tablespoons of butter to the same skillet over medium heat. Add the onions and cook for a couple of minutes, stirring to coat.
Add the mushrooms and 1/2 teaspoon of salt. Cook, stirring occasionally, until all the liquid evaporates and the mushrooms are browned - this will take about 10 minutes or so.
Add the flour and the tomato paste and stir well. Whisk in the beef broth and red wine. Bring the sauce to a boil and reduce to a simmer.
Return the salisbury steaks back to the pan in the simmering sauce. Cover the pan and cook for about 15 minutes, or until the internal temperature of the salisbury steaks reaches 165 degrees F.
Serve the salisbury steak and mushroom gravy over mashed potatoes.