01 - Preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside.
02 - In a mixing bowl, combine the sourdough discard, shredded cheddar, softened butter, sea salt, garlic powder, and smoked paprika. Stir until all ingredients are evenly incorporated.
03 - Gradually add the all-purpose flour to the mixture, stirring until a shaggy dough begins to form. Add cold water one tablespoon at a time, mixing gently, just until the dough comes together in a cohesive ball.
04 - Turn the dough out onto a lightly floured surface and knead gently until smooth and uniform, about 30 seconds. Avoid overworking the dough.
05 - Roll the dough out to an even 1/8-inch thickness. Using a sharp knife or pizza cutter, cut the sheet into 1-inch squares.
06 - Transfer the cut squares to the prepared baking sheet, spacing them about 1/2 inch apart. Prick each cracker once or twice with a fork and sprinkle lightly with coarse sea salt.
07 - Bake for 16 to 20 minutes, rotating the baking sheet halfway through, until the crackers are golden brown and crisp throughout.
08 - Transfer the crackers to a wire rack and allow them to cool completely. Store in an airtight container at room temperature for up to 1 week.