Sprinkle the gouda over your work surface. Lightly brush a rolling pin with flour. Roll out the dough to a 10-inch by 12-inch rectangle allowing the cheese to stick to the bottom of the dough. Brush the top with a little water and sprinkle on the rosemary.
Use a pizza cutter to cut long strips about ½-inch wide. Place the strips 1 inch apart on the prepared sheet pans. Twist each strip and lightly press down the edges. Chill in the refrigerator for 30 minutes.
Preheat the oven to 375 degrees F. Bake for 15-20 minutes until the straws are puffed and golden brown. Transfer to a wire rack to cool.
Serve warm or at room temperature. Straws are best eaten the day they are baked.