Melt butter over medium heat in medium pot.
Add gluten-free flour and salt, whisking constantly until all flour is absorbed. This may not create a thick paste at this point and that is ok. It should look kind of foamy and well mixed. This will take a minute or two.
While whisking, pour in whole milk. The cold temperature of the milk may cause your flour and butter mixture to clump. That is ok. Just keep whisking.
Bring milk to a slow boil. You do not want to walk away during this. You need to be whisking frequently, making sure you are scraping the bottom of the pot. Otherwise, the bottom will thicken and burn.
Once your mixture starts thickening* and bubbling add in shredded cheese and a pinch of pepper. Continue to whisk mixture until cheese is completely melted.
Turn off heat and top your favorite pasta, baked potato or even broccoli with it.