Fill a roasting pan with water. Carefully and evenly crack the matzo squares in half and add them to the pan with water. Submerge the matzos for 30 seconds, drain of excess water, transfer to a clean kitchen towel, loosely wrap and set aside for 5 minutes.

Meanwhile, combine the mayonnaise, ketchup and mustard in a small bowl and stir to combine. Set aside.

Place the matzos onto a flat work surface and gently press the ground beef to form an even layer across the entire surface. Generously season the meat side with salt and pepper.

Preheat a large cast-iron skillet over medium-high heat. Add the matzo, meat side-down, top with a burger press or small pan for even contact and cook, undisturbed, until deeply browned, around 90 seconds. Flip and cook the matzo side until golden and crispy, around 60 seconds.

Top the meat side with the prepared sauce, onion, pickles and lettuce. Fold over one side like your closing a book and serve immediately.