Preheat the oven to 350°F. Prepare a large baking pan by lining with parchment paper. Set aside.
In the bowl of a stand mixer, or using a hand mixer, beat together butter, cheese, sea salt, cayenne and paprika until fully incorporated. Scrape down the bowl and beat for another 10 seconds.
With the mixer on low, mix in the flour slowly until just incorpoated. You should have a soft, crumbly dough.
Load the dough into the cookie press (according to manufacturer's directions) fitted with a star-shaped disc. Hold the cookie press over the prepared baking pan and click the repeatedly to extrude long ropes of dough. Cut the ropes into desired size (about 2 inch bites are a good size) and carefully arrange on baking pan, leaving an inch or two between pieces.
Bake for about 12 minutes or until the dough has set and is lightly browning around the bottom.
Remove from oven and allow to cool (they will harden and crisp up as they cool). Serve or store once cooled.