Get a nice big Dutch oven and add enough peanut oil to be 2 inches deep. Install your candy/fry thermometer to the side of the pot and turn the heat to medium-high. Your thermal destination is 320°F.
Turn on your broiler and place rack in top position. This is a perfect time to use your toaster oven if you have one.
Meanwhile, place the meat and salt in the bowl of a food processor and pulse 10 times or until it resembles a medium grind.
Weigh out the meat into 4 (3-ounce) 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, but that’s good — those irregularities will become crunchy goodness. The meat will also shrink back down to bun-size as it cooks. Set smashed meat sheet aside and repeat flattening process with remainder of meat balls (leave the meet sheets inside the wax paper for now) and refrigerate.
Grate the cheese and toss with the paprika and garlic powder until all the powder has stuck to the cheese.
Spread a thin layer of mayo on the bottom of the buns and place half the cheese mixture on top. Spread mustard on the bun tops and place the rest of the cheese on top. So, you should have half the cheese on the bottoms (on mayo) and half on the tops (on mustard). Place both halves under the broiler so that the cheese melts as you cook the burgers. This will happen quickly, so don’t walk away.
When the oil hits 320°F, remove the meat patties from the refrigerator. One by one, transfer the meat patties by peeling back one piece of wax paper and inverting the patty onto a spider strainer. Peel back the other sheet of wax paper and gently lower the spider into the peanut oil, letting the patty float free. Cook one minute — no more, no less.You can cook up to three patties at a time, but don’t let the oil temperature drop below 300°F.
Remove the fried meat to a paper towel to drain briefly then place it on the bottom bun right away. Place the pickles on top, followed by the bun top. The goal: bread/mayo/cheese/meat/pickles/cheese/mustard/bread.
Consume immediately or wrap in foil to keep warm for up to 30 minutes.