Preheat oven to 400°F. In a food processor, combine the cheese, butter, 1 cup flour, salt and spices in five 5-second pulses until the mixture resembles coarse crumbs. Add the milk and process until dough forms a ball , about 10 seconds.
On a lightly floured surface, roll the dough into a rectangle until approximately 1/8-inch thick. Using a pizza wheel or a sharp knife, cut the dough into thin strips, about 1/4-inch wide. Transfer to an ungreased cookie sheet. Sprinkle with garlic powder if desired.
Bake on middle rack of oven for 12-15 minutes or until the cheese straws are slightly browned on the edges.
Remove from oven and set cookie sheet on rack to cool. Serve at room temperature.
Cheese straws will keep in a sealed container for two days.