"GYOB" (GRIND YOUR OWN BURGERS)

Steps:

• Place the beef chunks on a baking sheet in a single layer, leaving a little space around each piece. Freeze the meat until it's very firm and starting to harden around the edges but still pliable, 15 to 30 minutes. Freeze the blade of a food processor at the same time.
• Place half of the meat in the food processor fitted with the chilled blade and pulse until coarsely ground, 10 to 15 one-second pulses, stopping to redistribute the meat with a wooden spoon around the bowl as necessary to ensure even grinding. Turn out the meat onto a baking sheet (just dump it out - try not to touch the meat too much). Repeat the grinding with the remaining meat. Spread the meat on the baking sheet and inspect carefully, discarding any long strands of gristle or large chunks of hard meat or fat. Season the meat with salt and pepper.
• Divide the meat into 4 equal piles. Form the piles with your hands into 4 large thin patties, about 4 inches wide. The patties should be loosely packed.
• Heat a large cast-iron skillet or large heavy griddle pan over high heat. Spread the butter on the cut sides of the buns. Toast the buns in the skillet until golden brown, about 2 minutes.
• Working in two batches, add the beef patties to the skillet and immediately press them down once with a spatula; do not smoosh them again. Cook until crusty brown on the bottom, 4 to 5 minutes; flip once, top with a piece of cheese and cook until the other side is crusty and the cheese melts, about 4 more minutes. Place the burgers on the toasted buns; top with sliced avocado. Serve with steamed broccoli.