Put the softened cheese and butter in the bowl of a heavy-duty electric mixer. Using the heaviest mixer paddle attachment, beat until the mixture has the consistency of whipped cream, 15 to 30 minutes.
In a large bowl, sift 3 cups of the flour with the salt, black pepper, cayenne pepper and garlic powder. Gradually add the seasoned flour to the cheese mixture by large spoonfuls, beating well after each addition. Add the remaining 1 cup unseasoned flour incrementally until the dough is somewhat stiff but still soft enough to be pushed through a cookie press; you may not need to add all the flour.
Lightly spray 4 cookie sheets with cooking spray. Put a portion of the dough into a cookie press fitted with the star tube and press the dough onto a cookie sheet in long strips that run the length of the pan. Repeat until the pan is full. Bake until straws are golden brown and crisp, about 20 minutes.
With your hands or a sharp knife, break or cut the long strips into 3-inch lengths. Use a flat, thin spatula or an egg turner to remove the cheese strips from the pan. Allow them to cool on a wire rack. When they are completely cool, serve or store in a tightly covered container.
If you don't have a cookie press, form the dough into 1-inch balls and flatten them with a fork.
Recipe adapted from Georgia Cooking from an Oklahoma Kitchen by Trisha Yearwood (c) Clarkson Potter 2008