Begin by combining 3/4 cup of all-purpose flour, 12 ounces of lean ground beef, 1 teaspoon of garlic powder, and 1/2 teaspoon of ground black pepper in a large bowl. Add in 1 cup of whole buttermilk and mix until well combined without overworking the mixture. Shape the mixture into equal-sized oval patties, about 1 inch thick. In a separate shallow dish, combine 1 cup of whole milk with 1 tablespoon of balsamic vinegar. In another dish, create a mixture with 3/8 teaspoon of baking powder and enough all-purpose flour to coat the patties. Dip each patty in the milk mixture before coating them in the flour mixture.
Heat 1/2 inch of vegetable oil in a large skillet over medium-high heat. Once hot, carefully add the coated patties to the pan and fry until they turn a beautiful golden brown on both sides for around 3-4 minutes per side. After removing the patties from the pan, let them drain on a paper towel-lined plate. For an optional touch of heat, sprinkle 3/4 teaspoon of hot sauce on each patty.
Using the same skillet as before with only about 2 tablespoons of oil remaining in it, stir together 2 tablespoons of all-purpose flour for around one minute until combined well with the remaining oil. As you continue to stir, gradually add 2 cups of whole milk and cook until the mixture thickens to a gravy-like consistency. Season with 1/2 tablespoon of Italian seasoning and 3/4 teaspoon of kosher salt, adjusting to your preferred taste. For serving, top each hamburger steak patty with the prepared gravy and garnish with ground black pepper and chopped green onion for an added pop of flavor.