Step 1

To grind with a meat grinder: Place grinding shaft, feed tube, plate, die, and screw of a meat grinder into the freezer. Spread beef chunks evenly in a single layer on a large plate or rimmed baking sheet. Place in freezer and freeze until starting to get firm around edges but still malleable, about 20 minutes. Set up meat grinder with 3/8ths inch plate. Grind meat into a cold bowl. Working quickly, grind meat again using 1/4-inch plate. If grinder or meat begins to get too warm during grinding process, return to freezer for 10 minutes before continuing to grind.

Step 2

To grind with a food processor: Spread beef chunks evenly in a single layer on a large plate or rimmed baking sheet. Place in freezer and freeze until starting to get firm around edges but still malleable, about 20 minutes. Working in three batches, place meat cubes in the work bowl of a food processor. Pulse until finely chopped, about 15 to 20 short pulses. Transfer to a bowl and repeat with remaining beef.

Step 3

Form beef into four patties about 1/2-inch wider than the burger buns with a slight depression in the center to account for bulging as they cook. Season generously with salt and pepper and refrigerate until ready to cook.

Step 4

Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, spread evenly over one side of coal grate. Alternatively, set half the burners of a gas grill to high heat. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Clean and oil the grilling grate.

Step 5

Place burgers directly over hot coals, cover with vents open, and cook, turning occasionally, until well charred and center of burgers register 110°F on an instant read thermometer, about 5 minutes. Place cheese on top of burgers and continue to cook until cheese is melted and burgers register 125°F for medium rare or 135°F for medium, 1 to 2 minutes longer. Transfer burgers to a large plate.

Step 6

Toast buns over center of grill until golden brown and warmed through. Top burgers as desired, place in buns, and serve.