In your stand mixer, beat together the cheese and butter until creamy. You'll probably need to scrape it down several times to fully combine. This should take about five minutes.
Add in the salt. Gradually mix in the flour bit by bit, mixing constantly, until the dough is sandy-looking.
Gradually add in ice water about 1 Tsp at a time, until the dough comes together.
Divide the dough into two portions. Flatten them into thick discs and wrap them with plastic wrap. Chill in the fridge for at least an hour.
Preheat your oven to 375°F.
Working with about a third of a dough disc at a time, lightly flour your rolling pin and roll the dough flat, as thin as you can. At least ⅛th of an inch thick, if not thinner. The thinner you roll it, the less puffy the resulting crackers will be. Keep excess dough chilled when not working with it.
Cut your crackers into squares about an inch to a side, or slightly longer, as you prefer. The rough edges of the dough can be re-balled, re-rolled, and re-cut until you've used up all of the dough.
Using a skewer or chopstick, poke a hole in the center of the cracker squares. Line your baking sheet with parchment paper and arrange the crackers on it, leaving a tiny bit of space between them. They don't spread, so don't worry much as long as they aren't touching.
(OPTIONAL) For a more "authentic" Cheez-It, brush the crackers with a bit of oil and sprinkle kosher salt lightly across them. They're fine without it, though, if you want to cut down on the salt.
Bake each batch for 14 or so minutes, or until they look golden and crispy. Once done, move to a cooling rack ASAP to cool down. Repeat the process until you've baked all the dough.