In a large mixing bowl, combine your sourdough discard, all-purpose flour, shredded cheddar cheese, softened unsalted butter, and kosher salt. Mix until a cohesive and smooth dough forms, about 3-5 minutes.

Divide the dough into four equal pieces, shape into rectangles, wrap in plastic wrap, and refrigerate for 30 minutes.

Preheat your oven to 350°F (175°C). Roll out each piece of chilled dough to about 1/16-inch thick.

Brush each rolled-out dough with olive oil or melted butter. Cut the dough into 1-inch squares and poke holes in the center of each square.

Transfer cut crackers to a baking sheet lined with parchment paper and bake for 15-20 minutes until golden brown and crispy.

Allow the crackers to cool on the baking sheet for about 10 minutes before transferring to an airtight container.