In a food processor with a grate attachment, grate the potatoes, onion, celery, and parsley all together. Alternatively, you can grate them by hand with a box grater.
Transfer the mixture to a sieve and use your hands to squeeze out the juice as much as possible. You want the potatoes as dry as can be so they will be crispy.
Put the mixture into a medium bowl. Add the egg, flour, minced garlic, salt and pepper and stir until it’s well-mixed.
Cover the bottom of a medium-sized skillet with the oil and heat the oil over a medium- high heat.
Place about one-quarter cup of the mixture in your hand and form it into a ball.
Flatten the ball in your hand a little then place it in the pan and flatten it out a little more with a spatula.
Fry the latkes about 4 or 5 minutes on each side or until crispy and medium brown in color.
Place the latkes on a paper towel-lined plate to absorb any excess oil. Blot the tops of the latkes also with paper towels.
Serve immediately.