Heat the oil to 350 degrees F in a deep, heavy pot.
Set up a breading station with the flour and a pinch of salt and pepper in one pie pan; the beaten eggs in a second; and the pretzel crumbs in a third.
Dip each cheese stick in the flour, then in the egg wash, and then in the pretzels.
Carefully add the breaded cheese sticks to the hot oil and fry until dark golden brown all over, about 1 minute per side. Drain on a paper-towel-lined plate and immediately sprinkle with salt. Serve with salsa.