Cut the rib eye and chuck roast into 1-inch pieces. Toss these together in a large bowl and freeze for about 30 minutes while you set up your grinder. Grind the beef on a medium die. Give the ground meat a couple of hand tosses after combining and then divide into 4 (12 ounces) patties – we like to use metal ringers to lightly pack the meat into tall rounds.
Heat a large flat top (or cast iron skillet) to medium-high. Season the beef patties generously with kosher salt on all sides. Melt the beef tallow on the flattop and add the burger patties. Cook for 3 to 4 minutes on the first side, flip and cook for 3 to 4 minutes longer. Top each burger with a slice of american cheese and broil to melt it.
Toast the burger buns on the still hot flat top. Build the burger – bun, patty with cheese, thick sliced onion, top bun. That’s it!