In a large mixing bowl, combine the sourdough discard, flour, cheese, butter, and salt. Mix everything together and knead until a smooth dough forms.
1 cup (227 grams) sourdough starter discard, 1 cup (120 grams) all-purpose flour, 2 cups (200 grams) cheddar cheese, 2 tablespoons (28 grams) unsalted butter, ½ teaspoon (3 grams) kosher salt
Divide the dough into four equal pieces and shape them into rectangles. Wrap each piece tightly in plastic wrap and place them in the refrigerator for about 30 minutes.
Preheat your oven to 350°F.
After chilling, take one piece of dough out of the refrigerator. Place it on a lightly floured sheet of parchment paper. Sprinkle a little flour on top of the dough and your rolling pin. Roll the dough out into a large rectangle about 1/16-inch thick.
Brush the rolled-out dough lightly with olive oil or melted butter. Use a pizza cutter or sharp knife to cut the dough into roughly 1-inch squares. Use a chopstick or fork to poke holes in each cracker and sprinkle them with kosher salt. Repeat the process with the remaining pieces of dough.
Olive oil or melted butter, Additional kosher salt
Transfer the crackers onto a baking sheet, keeping them on the parchment paper. Bake the crackers in the preheated oven for 15-20 minutes or until they are golden brown and crisp. Keep an eye on them, as the outer crackers may bake faster and need to be removed before the center crackers.
Let the crackers cool on the baking sheets before transferring them to an airtight container for storage. Store at room temperature for up to one week.