Start dough. In a food processor, combine flours, sugar, salt, butter, and sourdough starter. Pulse until the mixture forms fine crumbs.
Slowly add water. Add ice water 1 tablespoon at a time, pulsing after each addition, just until the dough holds together when pressed.
Shape and chill.. Shape dough into a disc, wrap in plastic, and refrigerate at least 1 hour or up to 3 days.
Roll out thin. Preheat oven to 375°F. Roll dough between two floured sheets of parchment to 1/16 inch thick.
Cut. Trim edges and cut into 1½-inch squares with a pizza cutter. Transfer to a parchment-lined baking sheet.
Prick with fork. Use a fork to prick each cracker twice. Sprinkle with additional salt if desired.
Bake. Bake for 12–15 minutes until golden and dry to the touch. Cool completely on the pan.