01 - In a food processor, pulse the flour, fine sea salt, garlic powder, and smoked paprika several times until evenly combined.
02 - Add the cold diced butter and pulse until the mixture resembles coarse crumbs with no large butter pieces remaining.
03 - Add the grated sharp cheddar cheese to the food processor and pulse until it is evenly distributed throughout the mixture.
04 - Add the sourdough discard and pulse just until a cohesive dough comes together. Be careful not to overmix, as this can make the crackers tough.
05 - Turn the dough out onto a lightly floured surface and shape it into a flat disc. Wrap tightly in plastic wrap and refrigerate for at least 30 minutes to firm up.
06 - Preheat the oven to 350°F. Line two baking sheets with parchment paper and set aside.
07 - Roll the chilled dough out on a lightly floured surface to about 1/8 inch thickness. Using a knife or pizza cutter, cut the dough into 1-inch squares and transfer them to the prepared baking sheets, spacing about 1/2 inch apart.
08 - Prick each cracker once or twice with a fork to prevent puffing, then sprinkle lightly with flaky sea salt.
09 - Bake for 20 to 25 minutes, rotating the baking sheets halfway through, until the crackers are golden brown and crisp to the touch.
10 - Allow the crackers to cool completely on the baking sheets. They will continue to crisp as they cool. Store in an airtight container at room temperature.