Scrub the potatoes under water until totally clean. Use a mandolin or Japanese slicer to slice the potatoes as thinly as possible. As you slice them, submerge them in cold water and set aside. Mix together the garlic salt, paprika, black pepper, cayenne and salt in a small bowl and set aside.
In 2 heavy Dutch ovens, heat some vegetable oil to 375 degrees F (use a thermometer to keep the temp right!). Lay the potatoes on a baking sheet lined with paper towels, and blot them with more paper towels to dry completely.
Lower batches of potatoes into the oil using a spatula. They will fry very quickly, about 1 1/2 minutes; remove with a spatula when they're nice and golden and crisp. Immediately sprinkle on the spice mix. Repeat with the rest of the potatoes!