Add cheese mixture to flour mixture and mix with your hands until firm and pliable. (See notes.)
Using a cookie press: Using a cookie press fitted with a thin, ridged disk, pipe the cheese mixture in rows on the prepared baking sheet, spacing about 1 inch apart. Score the rows with a butter knife to create 1-inch to 2-inch wafers.
Without a cookie press: Roll the dough into 1/4-inch thickness on a clean work surface. Use a pastry wheel to cut the dough into straws about 1/2-inch wide by 1 to 2 inches long. Carefully transfer to the prepared baking sheet, spacing about 1 inch apart.
Bake until lightly browned, about 20 minutes. Let cool completely on baking sheet.
If you used a cookie press, cut the cheese straws apart along the score lines.
Transfer cooled cheese straws to a large airtight container lined with paper towels. Cover and store at room temperature for up to one week.
Notes
Rick does not recommend substituting butter in this recipe.
For mild cheese straws, use 2 teaspoons each of paprika and cayenne. For even spicier straws, use 2 tablespoons each of paprika and cayenne.
If mixing the dough by hand is not accessible for you, you can use a stand mixer fitted with the paddle attachment.