Add the meat to a large bowl. With your hands, mix in the onion, garlic, seasoning, 4 teaspoons Worcestershire sauce, black pepper and Parmesan cheese.
Shred 5 tablespoons of the stick of butter, and mix in.
Form the meat into 4 equal patties.
Melt 3 tablespoons of butter in a large cast iron skillet over medium heat. Add the patties and cook until nearly cooked through.
Remove the patties from the skillet (reserve the grease) and add the sliced onions. Continue cooking until the onions are tender, stirring occasionally.
Meanwhile, in a small bowl, whisk together the beef broth, half and half, onion powder, garlic powder and the remaining 2 teaspoons Worcestershire sauce. Stir the mixture into the onions and bring to a simmer.
In a small bowl, whisk together the water and cornstarch. Stir into the gravy mixture. Cook for about 2 to 3 minutes, or until the mixture begins to thicken, stirring occasionally.
Add the patties to the gravy and continue cooking for about 5 minutes, to allow the flavors to incorporate. Flip the burgers a couple times while cooking.
Remove from the heat. Serve with mashed potatoes.