In a stand mixer with paddle attachment, mix the softened butter, shredded cheese, salt, smoked paprika, cayenne, and rosemary together until creamy.
Add the flour and mix until just combined. It will be crumbly and that's okay! It should hold together if you squeeze a bit of it between your fingers.
Cover with plastic wrap and let the dough rest for about 30 minutes (I keep it in the bowl and just tuck the plastic wrap over the top of the dough).
Preheat your oven to 350 F. Roll the dough fairly thin (like 1/4-1/2 inch, not wafer thin) and cut into thin strips of your desired length. Place on a baking sheet lined with parchment paper. They will spread a tiny bit so leave a bit of space between. I use my scraper tool to both cut and move the dough, for ease.
Bake for about 15 minutes, until light brown and set. Allow to cool, then store in an airtight container.