Procedure: Get a nice big Dutch oven and add enough peanut oil to be two inches deep. Install your fry/candy thermometer to the side of the pot and crank the heat to medium-high. Your thermal destination is 320 degrees F.
Meanwhile. . .
Place the meat and the salt in the bowl of a food processor and pulse 10 times or until it resembles a medium grind.
Weigh the meat into four equal portions and roll into balls. Place one of the meat balls between two sheets of wax paper on a tortilla press and flatten completely into a 5- to 6-inch-wide disk. It will be irregular around the circumference and that's good as all those irregularities will become crunchy goodness. The meat will also shrink back down to bun-size as it cooks. Set the smashed meat sheet aside, replace the wax paper and repeat flattening process with the remainder of the meat balls, then refrigerate.
Grate the cheese, then toss with the garlic powder and paprika until all the powder has stuck to the cheese. (If the powder doesn't stick, let the cheese warm up a bit and toss again.)
Heat the broiler and place the rack in top third of oven. This is a perfect time to use your toaster oven if you have one. Arrange the bun halves cut-side up on a sheet pan. Spread a thin layer of mayo on the bottom halves and mustard on the tops, then cover both with the cheese mixture and broil briefly to melt the cheese. I wouldn't walk away as this will happen pretty quickly.
When the oil hits 320 degrees F, remove the meat patties from the refrigerator. Cook one at a time by peeling the wax paper from one side of the patty then flipping it onto the spider and peeling off the other piece of paper. Gently lower the spider into the fat and jiggle until the patty floats free. Cook one minute -- no more, no less. You can cook up to three patties at a time. . . but watch the oil temp and don't let it drop to under 300 degrees F.
Remove the fried meat to a paper towel and drain briefly, then transfer right away to the bun bottom. Top with the pickles then the bun top. The goal: bread/mayo/cheese/meat/pickles/cheese/mustard/bread.
Consume or wrap in aluminum foil and hold for up to 30 minutes.
If you prefer not to use peanut oil, safflower or canola are fine too. In a pinch you can use the smooth underside of a dinner plate, but the press is more precise and a lot more fun.