Prepare the Dough: In a mixing bowl, combine the sourdough discard, shredded cheddar cheese, softened butter, and salt. Mix until well combined. Gradually add the flour, mixing until a soft dough forms. If the dough is sticky, add a tablespoon of flour at a time until it becomes manageable.
Chill the Dough: Shape the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes. Chilling makes it easier to roll out and ensures the crackers hold their shape.
Preheat the Oven: Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Roll and Cut: On a floured surface, roll out the chilled dough to about ⅛-inch thickness. Using a pastry cutter, pizza wheel, or small square cookie cutter, cut the dough into 1-inch squares. Sprinkle with coarse sea salt. For the signature Cheez-It look, poke a small hole in the center of each square with a skewer or toothpick.
Bake: Transfer the squares to the prepared baking sheet, leaving a little space between them. Bake for 15–20 minutes, or until the crackers are golden and crisp. Keep an eye on them to prevent overbrowning.
Cool and Store: Allow the crackers to cool completely on a wire rack before storing them in an airtight container. They’ll stay fresh for up to a week.