Use the small holes of a box grater to grate the block of cheddar cheese.
Add the cheese, softened butter, and sourdough discard to a food processor and pulse a few times to blend completely.
Mix the dry ingredients in a separate small bowl, add to the food processor, and pulse until a ball of dough forms.
Pat the dough into a disc (it should feel like Play-Doh), wrap in plastic wrap, and refrigerate to rest and chill the dough for at least 30 minutes and up to a couple of days.
Preheat the oven to 350ºF (177ºC).
Roll the dough in between two large pieces of parchment paper into a large, thin rectangle less than ⅛" thick.
Use a pastry wheel to cut out 1" squares.
Separate the crackers, place them on baking sheets lined with parchment paper, and dock the centers with a small hole with the wooden dowel or toothpick.
Sprinkle the tops with flaky salt.
Bake one sheet at a time for 15-17 minutes or until the crackers are turning dark orange brown and crispy.
Cool on a wire rack and continue baking the rest of the crackers.
