01 - Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
02 - In a mixing bowl, mix sourdough discard, sharp cheddar, softened butter, sea salt, garlic powder, and smoked paprika until fully combined.
03 - Gradually incorporate all-purpose flour, mixing until a shaggy dough develops. Add cold water as necessary, 1 tablespoon at a time, to draw the dough together.
04 - Transfer mixture to a floured surface and knead gently until dough is smooth.
05 - Roll the dough to a 1/8-inch thickness. Slice into 1-inch squares using a sharp knife or pizza cutter.
06 - Arrange squares on the prepared baking sheet. Pierce each cracker with a fork and sprinkle with coarse sea salt.
07 - Bake for 16 to 20 minutes, or until golden and crisp, turning the tray midway for even color.
08 - Cool crackers on a wire rack before storing in an airtight container at room temperature for up to one week.