In the bowl of a stand mixer fitted with a paddle attachment, mix the cheese, butter, and salt on low speed until combined. Add the flour and mix on low until pebbly. Slowly add 2 tablespoons of the water and mix as the dough forms a ball. If needed, add the additional tablespoon of water a little at a time until the dough forms. Pat the dough into a disk, wrap with plastic wrap, and refrigerate for 1 hour.
Preheat oven to 375 degrees F. Line two baking sheets with parchment paper. Divide the dough into two pieces and roll each into a very thin 10x12-inch rectangle (the dough should be no more than ⅛-inch high). Using a fluted pastry wheel, cut the rectangles into 1-inch squares, then transfer them to the baking sheets.
Bake for 15 to 17 minutes, or until puffed and browning at the edges. Immediately move the crackers to wire racks to cool completely, then store in an airtight container for up to 1 week.