In a large mixing bowl, combine the top sirloin and brisket pieces. Season with salt and pepper to taste.
Shape the beef mixture into three equal-sized patties, making them slightly larger than the buns since they will shrink while cooking.
Heat a skillet or griddle over medium-high heat and add 1 tablespoon of vegetable oil. Once hot, place the patties on the skillet. Cook for about 4-5 minutes on one side, then flip and cook for an additional 3-4 minutes. In the last minute of cooking, place a slice of American cheese on each patty to melt.
While the beef is cooking, melt the unsalted butter in a separate pan over medium heat. Add the cut hamburger buns, cut-side down, and toast them until golden brown.
Now it’s time to layer your Homemade Big Mac. Start with the bottom bun, spread a generous amount of Russian dressing, add shredded iceberg lettuce, a patty with melted cheese, and pickles. Repeat the layers with the middle bun, and finish off with the top bun.