Process all three flours, salt, rosemary and diced butter in a food processor until crumbly.
Add 4 tablespoons ice-cold water until the dough forms a ball (add another 1-2 tablespoons if needed but start with 4 tablespoons).
Stir in the cheese and wrap the dough in cling wrap. Put into the freezer for 30 minutes.
Preheat oven to 200 degrees C. Line a baking tray with baking paper.
Roll the dough on a well floured work surface into a large rectangle about 15x30cm. Cut into 30 thin strips and roll into round sticks.
Lay the cheese straws on the baking tray 1cm apart from each other and bake in the preheated oven for 10-12 minutes until they are golden brown. Cool on a wire rack.